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Soliton Solutions for Quasilinear Schrödinger Equations [PDF]
Journal of Applied Mathematics, 2013 Summary: By using a change of variables, we get new equations, whose respective associated functionals are well defined in \(H^1(\mathbb R^N)\) and satisfy the geometric hypotheses of the mountain pass theorem. Using this fact, we obtain a nontrivial solution.
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Multi loop soliton solutions and their interactions in the Degasperis-Procesi equation
, 2012 In this article, we construct loop soliton solutions and mixed soliton - loop soliton solution for the Degasperis-Procesi equation. To explore these solutions we adopt the procedure given by Matsuno.
Constantin A +13 more
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Journal of Ocean Engineering and Science, 2023 Nonlinear evolution equations (NLEEs) are frequently employed to determine the fundamental principles of natural phenomena. Nonlinear equations are studied extensively in nonlinear sciences, ocean physics, fluid dynamics, plasma physics, scientific ...
Sachin Kumar +2 more
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Duke Mathematical Journal, 1992 The authors consider the \(N\)-soliton solution to the Korteweg-de Vries equation in the limit \(N \to \infty\) by careful investigation of the spectral and scattering properties of the Schrödinger operator associated to the KdV equation by the inverse scattering transform.
Gesztesy, F., Karwowski, W., Zhao, Z.
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Advances in Difference Equations, 2020 This paper investigates the Bogoyavlenskii–Kadomtsev–Petviashvili (BKP) equation by using Hirota’s direct method and the Kadomtsev–Petviashvili (KP) hierarchy reduction method.
Wenjuan Rui, Yufeng Zhang
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Solitons in coupled atomic-molecular Bose-Einstein condensates in a trap
, 2007 We consider coupled atomic-molecular Bose-Einstein condensate system in a quasi-one-dimensional trap. In the vicinity of a Feshbach resonance the system can reveal soliton-like behavior.
Abo-Shaeer J R +6 more
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Active Metamaterials with Tunable Shear Nonreciprocity and Nonlinear Dynamics
Advanced Science, EarlyView.Active gear‐based mechanical metamaterials enable simultaneous control of translational and torsional stiffnesses by 30–100×, break shear reciprocity under positive versus negative loads, broadly tune resonant frequencies, and offer programmable dynamic responses.
Xin Fang, Miao Yu, Dianlong Yu, Li Cheng
wiley +1 more source
Bright and Dark Soliton Solutions of the (2 + 1)-Dimensional Evolution Equations
Mathematical Modelling and Analysis, 2014 In this paper, we obtained the 1-soliton solutions of the (2+1)-dimensional Boussinesq equation and the Camassa–Holm–KP equation. By using a solitary wave ansatz in the form of sechp function, we obtain exact bright soliton solutions and another wave ...
Ahmet Bekir +3 more
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Partial Differential Equations in Applied Mathematics, 2023 Recently, mathematicians, engineers, and scientists have explored the unique characteristics and potential applications of multi-solitons, which is an expanding domain of study.
A. K. M. Kazi Sazzad Hossain +1 more
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Nonlocal Coupled HI-MKdV Systems
, 2019 We first study coupled Hirota-Iwao modified KdV (HI-mKdV) systems and give all possible local and nonlocal reductions of these systems. We then present Hirota bilinear forms of these systems and give one-soliton solutions of them with the help of ...
Pekcan, Aslı
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