Results 151 to 160 of about 824 (182)

Darboux transformation and multi-soliton solutions of Boussinesq–Burgers equation

Physics Letters A, 2005
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Li, Xuemei, Chen, Aihua
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The Novel Multi-Soliton Solutions of the MKdV–Sine Gordon Equations

Journal of the Physical Society of Japan, 2002
From the introduction: We consider the mKdV-sine Gordon equation \[ u_{xt}+ A\left(\tfrac 32 u^2_xu_{xx}+u_{xxx}\right) =B\sin u, \] \((A,B\) are real constants) and find new multi-soliton solutions by Hirota's direct method.
Chen, Dengyuan, Zhang, Dajun, Deng, Shufang   +2 more
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Multi soliton solution for the system of Coupled Korteweg-de Vries equations

Applied Mathematics and Computation, 2009
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A. S. Abdel Rady, E. S. Osman, Mohammed Khalfallah   +2 more
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Warning on multi-soliton solutions to Zakharov equations

Journal of Physics A: Mathematical and General, 1983
Summary: Although it has been usually recognised that the Zakharov equations in one dimension are not completely integrable, multi-soliton solutions to them have been published recently, where the direct methods developed by Hirota are used. It is shown that this result is incorrect.
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Multi-Soliton Solutions of the Generalized Sawada–Kotera Equation

Zeitschrift für Naturforschung A, 2016
Abstract Korteweg–de Vries (KdV)-type equations can describe the nonlinear phenomena in shallow water waves, stratified internal waves, and ion-acoustic waves in plasmas. In this article, the two-dimensional generalization of the Sawada–Kotera equation, one of the KdV-type equations, is discussed by virtue of the Bell polynomials and ...
Da-Wei Zuo, Hui-Xia Mo, Hui-Ping Zhou
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Exact multi-soliton solutions in nonlinear optical systems

Optics Communications, 2008
In this paper, we present the (1 + 1)-dimensional inhomogeneous nonlinear Schrodinger (NLS) equation, which describes propagation of optical waves in nonlinear optical systems exhibiting spatial inhomogeneity, inhomogeneous nonlinearity and gain or loss at the same time.
Ruiyu Hao, Guosheng Zhou
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Multi-Soliton Solutions of a Derivative Nonlinear Schrödinger Equation

Journal of the Physical Society of Japan, 1980
Using bilinear transform method, we confirm a result of Chen, Lee, and Liu that a derivative nonlinear Schrodinger equation i u t + u x x +2 i u * u u x =0 is integrable. Explicit formula of the N -soliton solution of a more general equation i u t +β u x x + i δ' u * u u x +δ u * u u =0, where β, δ' and δ are arbitrary real constants is presented.
Akira Nakamura, Hsing-Hen Chen
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Multi-soliton solutions of a variable-coefficient KdV hierarchy

Nonlinear Dynamics, 2014
In this paper, Hirota’s bilinear method is extended to a new KdV hierarchy with variable coefficients. As a result, one-soliton solution, two-soliton solution and three-soliton solutions are obtained, from which the uniform formula of $$N$$
Sheng Zhang, Bin Cai
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Extended multi-soliton solutions of the Einstein field equations

Classical and Quantum Gravity, 1998
Summary: Extended soliton solutions of the Einstein field equations obtained within the framework of Sibgatullin's integral method are further analysed. The authors write the metric defining such solutions in a concise form suitable for concrete applications.
Manko, Vladimir S., Ruiz, Eduardo
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The hierarchy of multi-soliton solutions of the derivative nonlinear Schr dinger equation

Journal of Physics A: Mathematical and General, 2003
Summary: We provide a relatively simple approach to Bäcklund transformations for the derivative nonlinear Schrödinger equation. By iteration it leads to compact \(N\)-soliton formulae both with asymptotically vanishing and non-vanishing amplitudes. The phenomenology of these solutions is discussed and illustrated in some detail.
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