The European Physical Journal B最新文献

Re-entrant localization transition, quantum butterfly and robust edge modes in aperiodic zig-zag ladder 非周期锯齿梯的可重入局域跃迁、量子蝴蝶和鲁棒边缘模式

IF 1.9 4区物理与天体物理

The European Physical Journal B Pub Date : 2026-11-06 DOI: 10.1140/epjb/s10051-026-01312-1

Sayan Bhattacharya, Rhiddha Acharjee, Atanu Nandy

引用次数: 0

IF 1.9 4区物理与天体物理

The European Physical Journal B Pub Date : 2026-11-05 DOI: 10.1140/epjb/s10051-026-01307-y

Wenqiang Liu, Yunqing Yang

引用次数: 0

Solitons in the nonlinear Schrödinger equation with the pseudo-Raman term, anti-diffusion gain and nonlinear loss 具有伪拉曼项的非线性Schrödinger方程中的孤子，反扩散增益和非线性损耗

IF 1.9 4区物理与天体物理

The European Physical Journal B Pub Date : 2026-11-04 DOI: 10.1140/epjb/s10051-026-01293-1

E. M. Gromov, B. A. Malomed

{"title":"Solitons in the nonlinear Schrödinger equation with the pseudo-Raman term, anti-diffusion gain and nonlinear loss","authors":"E. M. Gromov, B. A. Malomed","doi":"10.1140/epjb/s10051-026-01293-1","DOIUrl":"10.1140/epjb/s10051-026-01293-1","url":null,"abstract":"<div><p>We introduce a nonconservative nonlinear Schrödinger equation (NLSE) which includes additional nonlinear terms accounting for the pseudo-stimulated-Raman-scattering (pseudo-SRS) effect and cubic loss. An essentially novel feature of the model is the linear anti-diffusion gain, which leads to the obvious blow-up in the infinite or spatially periodic system. We consider the absorptive boundary conditions, which suppress the blow-up driven by effective convective instability in the setup. The NSLE model is derived, in the extended adiabatic approximation, from the underlying Zakharov’s system, which includes the viscosity term acting on its low-frequency component and the anti-diffusion gain in the high-frequency (HF) one. The latter term appears if the expansion, with respect to the deviation of the wavenumber, is performed not around the minimum-loss point (as in the usual situation), but around a maximum-losspoint. Dynamics of moving solitons in the model is addressed by means of analytical and numerical methods. The sech approximation for the soliton predicts it as a stable fixed point (FP) of the system of balance equations for the HF norm and wave momentum, derived in the moving reference frame. The FP’s attraction basin is identified too. The predictions are corroborated by direct simulations of the full NSLE with the absorptive boundary conditions.</p><h3>Graphical abstract</h3>\u0000<div><figure><div><div><picture><img></picture></div></div></figure></div></div>","PeriodicalId":787,"journal":{"name":"The European Physical Journal B","volume":"99 11","pages":""},"PeriodicalIF":1.9,"publicationDate":"2026-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149338240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Exact solutions and linear stability of a class of nonlinear evolution equations with fractional nonlinearity 一类分数阶非线性演化方程的精确解与线性稳定性

IF 1.9 4区物理与天体物理

The European Physical Journal B Pub Date : 2026-11-04 DOI: 10.1140/epjb/s10051-026-01296-y

Xiujuan Wang, Jingyun Lv, Yanbin Yin

{"title":"Exact solutions and linear stability of a class of nonlinear evolution equations with fractional nonlinearity","authors":"Xiujuan Wang, Jingyun Lv, Yanbin Yin","doi":"10.1140/epjb/s10051-026-01296-y","DOIUrl":"10.1140/epjb/s10051-026-01296-y","url":null,"abstract":"<div><p>This paper investigates the exact solutions and linear stability of a class of high-order non-linear evolution equations with fractional non-linearity. We mainly consider the case where the exponent takes <i>p</i>=2/<i>n</i> or <i>p</i>=4/<i>n</i> with <i>n</i> <span>(in)</span> N, including representative values (<i>p</i> <span>(in)</span>{1,2,1/2,2/3,2/5}). By employing the Jacobi elliptic function expansion method, various new localized exact solutions are derived, and their properties are analyzed in detail, providing a theoretical basis for practical applications. The dynamical behaviors and evolution characteristics of these solutions are visualized through graphical representations. Furthermore, the linear stability of constant solutions is discussed to reveal the effects of fractional non-linearity. Finally, Physics-Informed Neural Networks (PINNs) are utilized to approximate the analytical solutions. The numerical results demonstrate excellent agreement with the exact solutions, verifying the effectiveness of the proposed approach.</p><h3>Graphical abstract</h3>\u0000<div><figure><div><div><picture><source><img></source></picture></div></div></figure></div></div>","PeriodicalId":787,"journal":{"name":"The European Physical Journal B","volume":"99 11","pages":""},"PeriodicalIF":1.9,"publicationDate":"2026-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149338244","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Exploring the unstable non-linear Schrödinger equation: dynamical analysis and diverse optical soliton solutions 探索不稳定非线性Schrödinger方程：动力学分析和不同的光孤子解

IF 1.9 4区物理与天体物理

The European Physical Journal B Pub Date : 2026-11-02 DOI: 10.1140/epjb/s10051-026-01260-w

Ning Lu, Zhi-Yong Fan, Kang-Le Wang

{"title":"Exploring the unstable non-linear Schrödinger equation: dynamical analysis and diverse optical soliton solutions","authors":"Ning Lu, Zhi-Yong Fan, Kang-Le Wang","doi":"10.1140/epjb/s10051-026-01260-w","DOIUrl":"10.1140/epjb/s10051-026-01260-w","url":null,"abstract":"<div><p>This work focuses on the unstable non-linear Schrödinger equation, which is used to elaborate the propagation of ultra-short signals in fiber optics. In this work, the variational principle of the unstable non-linear Schrödinger equation is established using the semi-inverse method. By employing the Galilean transformation, the planar dynamical system of the unstable non-linear Schrödinger equation is constructed, and its Hamiltonian function, bifurcation analysis, chaotic behavior and sensitivity analysis are presented. Moreover, some new soliton solutions and periodic solutions of the unstable non-linear Schrödinger equation are derived using two excellent mathematical approaches, which are called <span>((H/K))</span>-expansion method and improved <span>(e^{ - Theta left( zeta right)})</span>-expansion method. These solutions hold practical significance in the respective physical fields. The internal structure and evolution are represented in three-dimensional, two-dimensional, and contour graphs. These graphs are generated with appropriate choice of parameters to emphasize some important features of waves.</p><h3>Graphical abstract</h3>\u0000<div><figure><div><div><picture><source><img></source></picture></div></div></figure></div></div>","PeriodicalId":787,"journal":{"name":"The European Physical Journal B","volume":"99 11","pages":""},"PeriodicalIF":1.9,"publicationDate":"2026-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149309860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Analytical solutions and discrete soliton prediction via symmetric difference enhanced PINNs with Lax-pair constraints for the (text {RVL}_{-}(alpha )) system 基于lax对约束的对称差分增强pinn的(text {RVL}_{-}(alpha ))系统解析解和离散孤子预测

IF 1.9 4区物理与天体物理

The European Physical Journal B Pub Date : 2026-10-30 DOI: 10.1140/epjb/s10051-026-01287-z

Pei-Xiao Li, Xiao-Yong Wen

{"title":"Analytical solutions and discrete soliton prediction via symmetric difference enhanced PINNs with Lax-pair constraints for the (text {RVL}_{-}(alpha )) system","authors":"Pei-Xiao Li, Xiao-Yong Wen","doi":"10.1140/epjb/s10051-026-01287-z","DOIUrl":"10.1140/epjb/s10051-026-01287-z","url":null,"abstract":"<p>The present study addresses the relativistic Volterra lattice system, denoted as <span>(text {RVL}_{-}(alpha ))</span> system, a key member of the relativistic Volterra lattice hierarchy, serving as a prototypical discrete integrable model for describing nonlinear wave dynamics and energy transfer in lattice structures. The present study focuses on four main aspects: (1) Our first focus is on the continuum limit and conservation laws of <span>(text {RVL}_{-}(alpha ))</span> system; (2) Employing the Lax pair, we construct the discrete generalized <span>((m, 2N-m))</span>-fold Darboux transformation (DT), which yields multi-soliton and higher-order rational solutions. Asymptotic analysis confirms that the two-soliton interaction is elastic, characterized by well-defined phase shifts, whereas the rational counterparts feature distinct singularity structures and trace patterns; (3) For more accurate soliton prediction, we extend our previously proposed symmetric difference enhanced physics-informed neural networks (SDE-PINNs) to Lax pair-constrained SDE-PINNs (Lax-SDE-PINNs), embedding both spatial and temporal Lax pair equations into the loss function, supplemented by symmetric difference data augmentation, RAR sampling and NTK-based weight balancing. Numerical simulations of one- and two-soliton solutions demonstrate low reconstruction errors and stable extrapolation, confirming the effectiveness of combining Lax pair-constraints with the SDE-PINNs enhancements. (4) For the inverse problem, we focus on recovering the parameter <span>(alpha )</span>. Comparative numerical tests demonstrate that, under the same experimental settings, the Lax-SDE-PINNs outperforms the traditional PINNs and SDE-PINNs, yielding more accurate predictions and better robustness. These findings contribute to a deeper understanding of the physical phenomena described by <span>(text {RVL}_{-}(alpha ))</span> system, and may inform future studies on related integrable lattice models.</p>","PeriodicalId":787,"journal":{"name":"The European Physical Journal B","volume":"99 10","pages":""},"PeriodicalIF":1.9,"publicationDate":"2026-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149339589","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Spatio-temporal fluctuations of accumulated activity in the Bak–Sneppen model baker - sneppen模式中累积活动的时空波动

IF 1.9 4区物理与天体物理

The European Physical Journal B Pub Date : 2026-10-29 DOI: 10.1140/epjb/s10051-026-01286-0

Rahul Chhimpa, Abha Singh, Avinash Chand Yadav

{"title":"Spatio-temporal fluctuations of accumulated activity in the Bak–Sneppen model","authors":"Rahul Chhimpa, Abha Singh, Avinash Chand Yadav","doi":"10.1140/epjb/s10051-026-01286-0","DOIUrl":"10.1140/epjb/s10051-026-01286-0","url":null,"abstract":"<p>We study fluctuations of the accumulated activity <span>(h(x, t))</span> in the Bak–Sneppen model of evolution. When the worst fitness occurs at <span>(x)</span> at time <span>(t)</span>, the activity becomes one, and <span>(h(x, t))</span> increases by one unit. The accumulated activity resembles a height profile as observed in the discrete models of kinetic rough interfaces. We employ the tools developed for roughness analysis and examine the structure factor, since it can reveal anomalous features. A systematic finite-time scaling yields the roughness exponent <span>(chi =1.94(7))</span> and the dynamical exponent <span>(z=2.44(8))</span>. We find the spectral roughness exponent <span>(chi _s = 0.72(3) < chi )</span>, indicating that the interface shows intrinsic anomalous behavior. The anisotropic version of the BS model also exhibits intrinsic anomalous behavior with different scaling exponents. We also examine the accumulated activity in a class of random walks that display qualitatively similar behavior.</p><p>The structure factor <span>(S(k,t) )</span> of the accumulated activity in the BS model. <span>(S(k, t))</span> exhibits two different regimes separated by a cutoff wavenumber, varying as <span>(sim t^{-1/z})</span>, where <span>(z)</span> is the dynamical exponent. In the low-wavenumber regime, the structure factor remains constant, but increases with time. On the other hand, <span>(S(k, t) )</span> decays in power law along with a time-dependent variation in the high-wavenumber regime.</p>","PeriodicalId":787,"journal":{"name":"The European Physical Journal B","volume":"99 10","pages":""},"PeriodicalIF":1.9,"publicationDate":"2026-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149339357","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Riemann–Hilbert approach to N-soliton solutions of the Kuralay-II equation with zero boundary conditions 零边界条件下kuraly - ii方程n孤子解的Riemann-Hilbert逼近

IF 1.9 4区物理与天体物理

The European Physical Journal B Pub Date : 2026-10-28 DOI: 10.1140/epjb/s10051-026-01269-1

Yapeng Sheng, Yongshuai Zhang, Mao-Hua Li

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Vibrational resonance in a dual-parametrically modulated Briggs–Rauscher system 双参数调制布里格斯-劳舍尔系统的振动共振

IF 1.9 4区物理与天体物理

The European Physical Journal B Pub Date : 2026-10-28 DOI: 10.1140/epjb/s10051-026-01274-4

F. G. Dazan, Y. J. F. Kpomahou

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Physics-informed neural networks for computing soliton solutions of high-order Sawada–Kotera and derivative Schrödinger equations 计算高阶Sawada-Kotera及其导数Schrödinger方程的孤子解的物理信息神经网络

IF 1.9 4区物理与天体物理

The European Physical Journal B Pub Date : 2026-10-27 DOI: 10.1140/epjb/s10051-026-01297-x

Jian Shao, Wei Hu, Hongyu Wu

{"title":"Physics-informed neural networks for computing soliton solutions of high-order Sawada–Kotera and derivative Schrödinger equations","authors":"Jian Shao, Wei Hu, Hongyu Wu","doi":"10.1140/epjb/s10051-026-01297-x","DOIUrl":"10.1140/epjb/s10051-026-01297-x","url":null,"abstract":"<p>Physics-informed neural networks (PINNs) with a self-adaptive mechanism are employed to accurately solve the high-order Sawada–Kotera equation, achieving relative <span>(L_2)</span>-norm errors on the order of <span>(10^{-5})</span>. This represents a one-to-two order-of-magnitude improvement in accuracy over previously reported results for various soliton molecule solutions of the Sawada–Kotera equation. Moreover, the simulation domains are enlarged by two to three orders of magnitude while maintaining high prediction accuracy for the SK equation. Despite the substantially larger domains, the computational cost remains comparable, benefiting from the self-adaptive weighting mechanism and the mesh-free framework enabled by automatic differentiation. The proposed model also accurately solves genuine rational soliton solutions of the derivative Schrödinger equation, achieving relative <span>(L_2)</span>-norm errors on the order of <span>(10^{-5})</span>. This corresponds to a two-to-three order-of-magnitude improvement in accuracy over previous results, despite the considerably larger simulation domains.</p>","PeriodicalId":787,"journal":{"name":"The European Physical Journal B","volume":"99 10","pages":""},"PeriodicalIF":1.9,"publicationDate":"2026-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149339187","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0