The Nonlinear Schrödinger Equation [Working Title]最新文献

{"title":"A Comparison of the Undetermined Coefficient Method and the Adomian Decomposition Method for the Solutions of the Sasa-Satsuma Equation","authors":"M. Asma","doi":"10.5772/intechopen.101817","DOIUrl":"https://doi.org/10.5772/intechopen.101817","url":null,"abstract":"This chapter will talk about the mathematical as well as numerical aspects of the Sasa-Satsuma equation that is the extended nontrivial version of nonlinear Schrödinger’s equation. The exact solution will be found out by the undetermined coefficient method. After that, the Adomian decomposition method is secure numerical simulations of computed analytical solutions. The error plots are given to see the accuracy of the results.","PeriodicalId":184064,"journal":{"name":"The Nonlinear Schrödinger Equation [Working Title]","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115195767","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":"Soliton Like-Breather Induced by Modulational Instability in a Generalized Nonlinear Schrödinger Equation","authors":"S. Abdoulkary, A. Mohamadou","doi":"10.5772/intechopen.100522","DOIUrl":"https://doi.org/10.5772/intechopen.100522","url":null,"abstract":"We consider the nonlinear Schrödinger equation modified by a rational nonlinear term. The model appears in various studies often in the context of the Ginzburg-Landau equation. We investigate modulational instability by means of a linear stability analysis and show how the nonlinear terms affect the growth rate. This analytical result is confirmed by a numerical simulation. The latter analysis shows that breather-like solitons are generated from the instability, and the effects of the nonlinear terms are again clearly seen. Moreover, by employing an auxiliary-equation method we obtain kink and anti-kink soliton as analytical solutions. Our theoretical solution is in good agreement with our numerical investigation.","PeriodicalId":184064,"journal":{"name":"The Nonlinear Schrödinger Equation [Working Title]","volume":"89 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131225363","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":"Traveling Wave Solutions and Chaotic Motions for a Perturbed Nonlinear Schrödinger Equation with Power-Law Nonlinearity and Higher-Order Dispersions","authors":"Mati Youssoufa, O. Dafounansou, Camus Gaston Latchio Tiofack, A. Mohamadou","doi":"10.5772/intechopen.100396","DOIUrl":"https://doi.org/10.5772/intechopen.100396","url":null,"abstract":"This chapter aims to study and solve the perturbed nonlinear Schrödinger (NLS) equation with the power-law nonlinearity in a nano-optical fiber, based upon different methods such as the auxiliary equation method, the Stuart and DiPrima’s stability analysis method, and the bifurcation theory. The existence of the traveling wave solutions is discussed, and their stability properties are investigated through the modulational stability gain spectra. Moreover, the development of the chaotic motions for the systems is pointed out via the bifurcation theory. Taking into account an external periodic perturbation, we have analyzed the chaotic behavior of traveling waves through quasiperiodic route to chaos.","PeriodicalId":184064,"journal":{"name":"The Nonlinear Schrödinger Equation [Working Title]","volume":"319 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114471337","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":"Resonant Optical Solitons in (3 + 1)-Dimensions Dominated by Kerr Law and Parabolic Law Nonlinearities","authors":"Khalil S. Al-Ghafri","doi":"10.5772/intechopen.100469","DOIUrl":"https://doi.org/10.5772/intechopen.100469","url":null,"abstract":"This study investigates the optical solitons of of (3+1)-dimensional resonant nonlinear Schrödinger (3D-RNLS) equation with the two laws of nonlinearity. The two forms of nonlinearity are represented by Kerr law and parabolic law. Based on complex transformation, the traveling wave reduction of the governing model is derived. The projective Riccati equations technique is applied to obtain the exact solutions of 3D-RNLS equation. Various types of waves that represent different structures of optical solitons are extracted. These structures include bright, dark, singular, dark-singular and combined singular solitons. Additionally, the obliquity effect on resonant solitons is illustrated graphically and is found to cause dramatic variations in soliton behaviors.","PeriodicalId":184064,"journal":{"name":"The Nonlinear Schrödinger Equation [Working Title]","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116007454","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":"Nonlinear Generalized Schrödinger’s Equations by Lifting Hamilton-Jacobi’s Formulation of Classical Mechanics","authors":"G. Gouesbet","doi":"10.5772/intechopen.100068","DOIUrl":"https://doi.org/10.5772/intechopen.100068","url":null,"abstract":"It is well known that, by taking a limit of Schrödinger’s equation, we may recover Hamilton-Jacobi’s equation which governs one of the possible formulations of classical mechanics. Conversely, we may start from the Hamilton-Jacobi’s equation and, by using a lifting principle, we may reach a set of nonlinear generalized Schrödinger’s equations. The classical Schrödinger’s equation then occurs as the simplest equation among the set.","PeriodicalId":184064,"journal":{"name":"The Nonlinear Schrödinger Equation [Working Title]","volume":"167 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114185313","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":"From Schrödinger Equation to Quantum Conspiracy","authors":"F. T. Yu","doi":"10.5772/intechopen.99484","DOIUrl":"https://doi.org/10.5772/intechopen.99484","url":null,"abstract":"Schrödinger’s quantum mechanics is a legacy of Hamiltonian’s classical mechanics. But Hamiltonian mechanics was developed from an empty space paradigm, for which Schrödinger’s equation is a timeless (t = 0) or time-independent deterministic equation, which includes his fundamental principle of superposition. When one is dealing Schrödinger equation, it is unavoidable not to mention about Schrödinger ‘s cat. Which is one of the most elusive cats in modern science since disclosed the half-life cat hypothesis in 1935. The cat is alive or not had been debated by score of world renounced scientists it is still debating. Yet I will show Schrödinger ‘s hypothesis is not a physically realizable hypothesis, for which it has nothing for us to debate about. But quantum communication and computing rely on qubit information algorithm, I will show that qubit information logic is as elusive as Schrödinger’s cat. It exists only within an empty space, but not exists within our temporal (t > 0) universe. Since there is always a price to pay within our universe, I will show that every physical subspace needs a section of time ∆t and an amount of energy ∆E to create and it is not free. Although, double slit hypothesis had been fictitiously confirmed that superposition principle exists, but I will show that double-slit postulation is another non-physically realizable hypothesis that had let us to believing superposition principle is actually existed within our time–space. Yet one of the worst coverup must be particles behaved differently within a micro space to justify the spooky superposition principle, which is one of greatest quantum conspiracy in modern science. Nevertheless, the art of quantum mechanics is all about a physically realizable equation, we see that everything existed within our universe, no matter how small it is, it has to be temporal (t > 0) which includes all the laws, principles, and equations. Otherwise, it is virtual as mathematics is since Schrodinger equation is mathematics, but mathematics is not equaled to science. Finally, when science turns to virtual reality for solution it is not a reliable answer. But when science turns to physical reality for an answer it is a reliable solution.","PeriodicalId":184064,"journal":{"name":"The Nonlinear Schrödinger Equation [Working Title]","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133940941","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}