{"title":"Global Bifurcations in a Damped-Driven Diatomic Granular Crystal","authors":"D. Pozharskiy, I. G. Kevrekidis, P. G. Kevrekidis","doi":"arxiv-2407.19347","DOIUrl":"https://doi.org/arxiv-2407.19347","url":null,"abstract":"We revisit here the dynamics of an engineered dimer granular crystal under an\u0000external periodic drive in the presence of dissipation. Earlier findings\u0000included a saddle-node bifurcation, whose terminal point initiated the\u0000observation of chaos; the system was found to exhibit bistability and potential\u0000quasiperiodicity. We now complement these findings by the identification of\u0000unstable manifolds of saddle periodic solutions (saddle points of the\u0000stroboscopic map) within the system dynamics. We unravel how homoclinic tangles\u0000of these manifolds lead to the appearance of a chaotic attractor, upon the\u0000apparent period-doubling bifurcations that destroy invariant tori associated\u0000with quasiperiodicity. These findings complement the earlier ones, offering\u0000more concrete insights into the emergence of chaos within this\u0000high-dimensional, experimentally accessible system.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141864602","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Solitary Waves and Interacting Longons in Galerkin-truncated Systems","authors":"Jian-Zhou Zhu","doi":"arxiv-2407.20277","DOIUrl":"https://doi.org/arxiv-2407.20277","url":null,"abstract":"The compacton, peakon, and Burgers-Hopf equations regularized by the Galerkin\u0000truncation preserving finite Fourier modes are found to support new travelling\u0000waves and interacting solitonic structures amidst weaker less-ordered\u0000components (`longons'). Different perspectives focusing on the zero-Hamiltonian\u0000solitonic, chaotic-looking, and stationary longons are also offered.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"197 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141864605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Avinash Khare, Fred Cooper, John F. Dawson, Efstathios G. Charalampidis, Avadh Saxena
{"title":"Solitary waves in the coupled nonlinear massive Thirring as well as coupled Soler models with arbitrary nonlinearity","authors":"Avinash Khare, Fred Cooper, John F. Dawson, Efstathios G. Charalampidis, Avadh Saxena","doi":"arxiv-2407.16596","DOIUrl":"https://doi.org/arxiv-2407.16596","url":null,"abstract":"Motivated by the recent introduction of an integrable coupled massive\u0000Thirring model by Basu-Mallick et al, we introduce a new coupled Soler model.\u0000Further we generalize both the coupled massive Thirring and the coupled Soler\u0000model to arbitrary nonlinear parameter $kappa$ and obtain exact solitary wave\u0000solutions in both cases. Remarkably, it turns out that in both the models,\u0000because of the conservation laws of charge and energy, the exact solutions we\u0000find seem to not depend on how we parameterize them, and the charge density of\u0000these solutions is related to the charge density of the single field solutions\u0000found earlier by a subset of the present authors. In both the models, a\u0000nonrelativistic reduction of the equations leads to the same conclusion that\u0000the solutions are proportional to those found in the one component field case.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141770815","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Defect interactions in the non-reciprocal Cahn-Hilliard model","authors":"Navdeep Rana, Ramin Golestanian","doi":"arxiv-2407.16547","DOIUrl":"https://doi.org/arxiv-2407.16547","url":null,"abstract":"We present a computational study of the pairwise interactions between defects\u0000in the recently introduced non-reciprocal Cahn-Hilliard model. The evolution of\u0000a defect pair exhibits dependence upon their corresponding topological charges,\u0000initial separation, and the non-reciprocity coupling constant $alpha$. We find\u0000that the stability of isolated topologically neutral targets significantly\u0000affects the pairwise defect interactions. At large separations, defect\u0000interactions are negligible and a defect pair is stable. When positioned in\u0000relatively close proximity, a pair of oppositely charged spirals or targets\u0000merge to form a single target. At low $alpha$, like-charged spirals form\u0000rotating bound pairs, which are however torn apart by spontaneously formed\u0000targets at high $alpha$. Similar preference for charged or neutral solutions\u0000is also seen for a spiral target pair where the spiral dominates at low\u0000$alpha$, but concedes to the target at large $alpha$. Our work sheds light on\u0000the complex phenomenology of non-reciprocal active matter systems when their\u0000collective dynamics involves topological defects.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"37 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141770816","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Gino Biondini, Gennady A. El, Xu-Dan Luo Jeffrey Oregero, Alexander Tovbis
{"title":"Breather gas fission from elliptic potentials in self-focusing media","authors":"Gino Biondini, Gennady A. El, Xu-Dan Luo Jeffrey Oregero, Alexander Tovbis","doi":"arxiv-2407.15758","DOIUrl":"https://doi.org/arxiv-2407.15758","url":null,"abstract":"We present an analytical model of integrable turbulence in the focusing\u0000nonlinear Schr\"odinger (fNLS) equation, generated by a one-parameter family of\u0000finite-band elliptic potentials in the semiclassical limit. We show that the\u0000spectrum of these potentials exhibits a thermodynamic band/gap scaling\u0000compatible with that of soliton and breather gases depending on the value of\u0000the elliptic parameter m of the potential. We then demonstrate that, upon\u0000augmenting the potential by a small random noise (which is inevitably present\u0000in real physical systems), the solution of the fNLS equation evolves into a\u0000fully randomized, spatially homogeneous breather gas, a phenomenon we call\u0000breather gas fission. We show that the statistical properties of the breather\u0000gas at large times are determined by the spectral density of states generated\u0000by the unperturbed initial potential. We analytically compute the kurtosis of\u0000the breather gas as a function of the elliptic parameter m, and we show that it\u0000is greater than 2 for all non-zero m, implying non-Gaussian statistics.\u0000Finally, we verify the theoretical predictions by comparison with direct\u0000numerical simulations of the fNLS equation. These results establish a link\u0000between semiclassical limits of integrable systems and the statistical\u0000characterization of their soliton and breather gases.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141770817","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Radiation-like Shock Waves in Kink Scattering","authors":"Xiang Li, Lingxiao Long","doi":"arxiv-2407.14479","DOIUrl":"https://doi.org/arxiv-2407.14479","url":null,"abstract":"We study the radiation in kink collision via a model that varies between\u0000$phi^6$ theory and $phi^2$ theory with some discontinuities. Both numerical\u0000and analytical methods were used to investigate The kink-antikink(KAK) and\u0000antikink-kink(AKK) collision. In the numerical analysis, we found the critical\u0000velocities in both collisions increased with $n$. We also found a finite\u0000lifetime oscillon window in KAK collision for $n=2$. In the analytical part, we\u0000found a family of shock wave solutions that describes radiation in the kink\u0000collision perfectly. Moreover, an analytical AKK solution at\u0000$nrightarrowinfty$ and $v=1$ was found by considering a certain limit of\u0000these solutions.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"55 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740142","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Martina Chirilus-Bruckner, Jesús Cuevas-Maraver, Panayotis G. Kevrekidis
{"title":"Stability of Breathers for a Periodic Klein-Gordon Equation","authors":"Martina Chirilus-Bruckner, Jesús Cuevas-Maraver, Panayotis G. Kevrekidis","doi":"arxiv-2407.10766","DOIUrl":"https://doi.org/arxiv-2407.10766","url":null,"abstract":"The existence of breather type solutions, i.e., periodic in time,\u0000exponentially localized in space solutions, is a very unusual feature for\u0000continuum, nonlinear wave type equations. Following an earlier work [Comm.\u0000Math. Phys. {bf 302}, 815-841 (2011)], establishing a theorem for the\u0000existence of such structures, we bring to bear a combination of\u0000analysis-inspired numerical tools that permit the construction of such wave\u0000forms to a desired numerical accuracy. In addition, this enables us to explore\u0000their numerical stability. Our computations show that for the spatially\u0000heterogeneous form of the $phi^4$ model considered herein, the breather\u0000solutions are generically found to be unstable. Their instability seems to\u0000generically favor the motion of the relevant structures. We expect that these\u0000results may inspire further studies towards the identification of stable\u0000continuous breathers in spatially-heterogeneous, continuum nonlinear wave\u0000equation models.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
J. D'Ambroise, W. Wang, C. Ticknor, R. Carretero-González, P. G. Kevrekidis
{"title":"Stability and dynamics of massive vortices in two-component Bose-Einstein condensates","authors":"J. D'Ambroise, W. Wang, C. Ticknor, R. Carretero-González, P. G. Kevrekidis","doi":"arxiv-2407.10324","DOIUrl":"https://doi.org/arxiv-2407.10324","url":null,"abstract":"The study of structures involving vortices in one component and bright\u0000solitary waves in another has a time-honored history in two-component atomic\u0000Bose-Einstein condensates. In the present work, we revisit this topic extending\u0000considerations well-past the near-integrable regime of nearly equal scattering\u0000lengths. Instead, we focus on stationary states and spectral stability of such\u0000structures for large values of the inter-component interaction coefficient. We\u0000find that the state can manifest dynamical instabilities for suitable parameter\u0000values. We also explore a phenomenological, yet quantitatively accurate upon\u0000suitable tuning, particle model which, in line also with earlier works, offers\u0000the potential of accurately following the associated stability and dynamical\u0000features. Finally, we probe the dynamics of the unstable vortex-bright\u0000structure, observing an unprecedented, to our knowledge, instability scenario\u0000in which the oscillatory instability leads to a patch of vorticity that harbors\u0000and eventually ejects multiple vortex-bright structures.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"38 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719065","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Futai Hu, Abhinav Kumar Vinod, Wenting Wang, Hsiao-Hsuan Chin, James F. McMillan, Ziyu Zhan, Yuan Meng, Mali Gong, Chee Wei Wong
{"title":"Spatio-temporal breather dynamics in microcomb soliton crystals","authors":"Futai Hu, Abhinav Kumar Vinod, Wenting Wang, Hsiao-Hsuan Chin, James F. McMillan, Ziyu Zhan, Yuan Meng, Mali Gong, Chee Wei Wong","doi":"arxiv-2407.10213","DOIUrl":"https://doi.org/arxiv-2407.10213","url":null,"abstract":"Solitons, the distinct balance between nonlinearity and dispersion, provide a\u0000route toward ultrafast electromagnetic pulse shaping, high-harmonic generation,\u0000real-time image processing, and RF photonic communications. Here we newly\u0000explore and observe the spatio-temporal breather dynamics of optical soliton\u0000crystals in frequency microcombs, examining spatial breathers, chaos\u0000transitions, and dynamical deterministic switching in nonlinear measurements\u0000and theory. To understand the breather solitons, we describe their dynamical\u0000routes and two example transitional maps of the ensemble spatial breathers,\u0000with and without chaos initiation. We elucidate the physical mechanisms of the\u0000breather dynamics in the soliton crystal microcombs, in the interaction plane\u0000limit cycles and in the domain-wall understanding with parity symmetry breaking\u0000from third order dispersion. We present maps of the accessible nonlinear\u0000regions, the breather frequency dependences on third order dispersion and\u0000avoided mode crossing strengths, and the transition between the collective\u0000breather spatiotemporal states. Our range of measurements matches well with our\u0000first-principles theory and nonlinear modeling. To image these soliton\u0000ensembles and their breathers, we further constructed panoramic temporal\u0000imaging for simultaneous fast and slow axis two dimensional mapping of the\u0000breathers. In the phase differential sampling, we present two dimensional\u0000evolution maps of soliton crystal breathers, including with defects, in both\u0000stable breathers and breathers with drift. Our fundamental studies contribute\u0000to the understanding of nonlinear dynamics in soliton crystal complexes, their\u0000spatiotemporal dependences, and their stability-existence zones.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"132 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Alina Barbara Steinberg, Fabian Maucher, Svetlana Gurevich, Uwe Thiele
{"title":"Localized States in Dipolar Bose-Einstein Condensates: To be or not to be of second order","authors":"Alina Barbara Steinberg, Fabian Maucher, Svetlana Gurevich, Uwe Thiele","doi":"arxiv-2407.09177","DOIUrl":"https://doi.org/arxiv-2407.09177","url":null,"abstract":"We report the existence of localized states in dipolar Bose-Einstein\u0000condensates confined to a tubular geometry. We first perform a bifurcation\u0000analysis to track their emergence in a one-dimensional domain for numerical\u0000feasibility and find that localized states can become the ground state in\u0000suitable parameter regions. Their existence for parameters featuring a\u0000supercritical primary bifurcation shows that the latter is not sufficient to\u0000conclude that the phase transition is of second order, hence density\u0000modulations can jump rather than emerging gradually. Finally, we show that\u0000localized states also exist in a three-dimensional domain.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719068","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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