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Solitons in the noisy Burgers equation [PDF]
Physical Review E, 2001 We investigate numerically the coupled diffusion-advective type field equations originating from the canonical phase space approach to the noisy Burgers equation or the equivalent Kardar-Parisi-Zhang equation in one spatial dimension.
Axel Brandenburg +28 more
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Forced Soliton Equation and Semiclassical Soliton Form Factors [PDF]
Physical Review Letters, 2020 We show that the leading semiclassical behavior of soliton form factors at arbitrary momentum transfer is controlled by solutions to a new wave-like integro-differential equation that describes solitons undergoing acceleration. We work in the context of two-dimensional linear sigma models with kink solitons for concreteness, but our methods are purely ...
Ilarion V. Melnikov +2 more
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Soliton solutions by means of Hirota bilinear forms
Partial Differential Equations in Applied Mathematics, 2022 The paper aims to provide a brief overview of soliton solutions obtained through the Hirota direct method. A bilinear formulation of soliton solutions in both (1+1)-dimensions and (2+1)-dimensions is discussed, together with applications to various ...
Wen-Xiu Ma
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Assorted soliton solutions to the nonlinear dispersive wave models in inhomogeneous media
Results in Physics, 2022 The Sharma-Tasso-Olver and Klein–Gordon equations are significant models to interpret plasma physics, relativistic physics, quantum mechanics, nonlinear optics, etc.
M. Ali Akbar +3 more
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Rational soliton solutions of nonlocal multicomponent nonlinear Schrödinger equations
Partial Differential Equations in Applied Mathematics, 2022 In this paper, we present a generalized Darboux transformation for nonlocal multicomponent nonlinear Schrödinger (NLS) equations. Also, we provide a unified formula for Nth-order rational soliton solution of discussed nonlocal multicomponent NLS ...
Li-Na Zheng, Yu-Shan Bai
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Journal of Ocean Engineering and Science, 2023 This article considers time-dependent variable coefficients (2+1) and (3+1)-dimensional extended Sakovich equation. Painlevé analysis and auto-Bäcklund transformation methods are used to examine both the considered equations.
Shailendra Singh, S. Saha Ray
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Results in Physics, 2020 The Riemann wave equation and the Novikov-Veselov equation are interesting nonlinear equations in the sphere of tidal and tsunami waves in ocean, river, ion and magneto-sound waves in plasmas, electromagnetic waves in transmission lines, homogeneous and ...
Hemonta Kumar Barman +3 more
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The Translating Soliton Equation [PDF]
, 2021 We give an analytic approach to the translating soliton equation with a special emphasis in the study of the Dirichlet problem in convex domains of the plane.
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Journal of Taibah University for Science, 2023 Nonlinear features are revealed by one of the most competent and powerful approaches, i.e. soliton theory. The present article starts with the dust collisionless magnetized plasma where electrons are following double spectral [Formula: see text ...
Uday Narayan Ghosh
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A study on the compatibility of the generalized Kudryashov method to determine wave solutions
Propulsion and Power Research, 2021 In this article, we establish solitary wave solutions to the Estevez-Mansfield-Clarkson (EMC) equation and the coupled sine-Gordon equations which are model equations to analyze the formation of shapes in liquid drops, surfaces of negative constant ...
Hemonta Kumar Barman +2 more
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