Results 91 to 100 of about 49,111 (193)

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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Spectral conservation laws for periodic nonlinear equations of the Melnikov type

, 2008
We consider the nonlinear equations obtained from soliton equations by adding self-consistent sources. We demonstrate by using as an example the Kadomtsev-Petviashvili equation that such equations on periodic functions are not isospectral.
Grinevich, P. G., Taimanov, I. A.
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The String Equation and Solitons [PDF]

, 1996
9 pages, Based on lectures delivered at the Erice Chalonge School, `String Gravity and Physics at the Planck Scale', 8-19 September ...
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A (2 + 1)-Dimensional Integrable Breaking Soliton Equation and Its Algebro-Geometric Solutions

Mathematics
A new (2 + 1)-dimensional breaking soliton equation with the help of the nonisospectral Lax pair is presented. It is shown that the compatible solutions of the first two nontrivial equations in the (1 + 1)-dimensional Kaup–Newell soliton hierarchy ...
Xiaohong Chen, Tiecheng Xia, Liancheng Zhu   +2 more
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The simplified Hirota’s method for studying three extended higher-order KdV-type equations

Journal of Ocean Engineering and Science, 2016
In this work we study three extended higher-order KdV-type equations. The Lax-type equation, the Sawada–Kotera-type equation and the CDG-type equation are derived from the extended KdV equation.
Abdul-Majid Wazwaz
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Geometrical representation and Hirota direct approach for multiple soliton solutions of nonlinear M-coupled fractional equations

Mathematical and Computer Modelling of Dynamical Systems
This paper introduces a novel analytical framework for deriving multiple soliton and singular soliton solutions to M-coupled fractional evolution equations.
Abaker A. Hassaballa, Mehmet Yavuz, Emad A.-B. Abdel-Salam, Gassan A.M.O. Farah, Ibtisam Daqqa   +4 more
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Dynamical behavior of kink solitons in nonlinear Chaffee-Infante equations with chaotic and bifurcation analysis

Ain Shams Engineering Journal
The Chaffee-Infante Equations (CIEs) are modified types of reaction-diffusion equations which are frequently employed in research of phase transitions, pattern generation and nonlinear wave dynamics.
Zainab Alsheekhhussain, Tariq S. Alshammari, Yaouba Amadou, Saleh Alshammari, Mohammad Alshammari, M. Mossa Al-sawalha   +5 more
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Chaotic Phenomena, Sensitivity Analysis, Bifurcation Analysis, and New Abundant Solitary Wave Structures of The Two Nonlinear Dynamical Models in Industrial Optimization

Mathematics
In this research, we discussed the different chaotic phenomena, sensitivity analysis, and bifurcation analysis of the planer dynamical system by considering the Galilean transformation to the Lonngren wave equation (LWE) and the (2 + 1)-dimensional ...
M. Mamun Miah, Faisal Alsharif, Md. Ashik Iqbal, J. R. M. Borhan, Mohammad Kanan   +4 more
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Further quality analytical investigation on soliton solutions of some nonlinear PDEs with analyses: Bifurcation, sensitivity, and chaotic phenomena

Alexandria Engineering Journal
In this investigation, the analytical behavior of two prominent nonlinear wave equations, namely the doubly dispersive equation (DDE) and the Ablowitz-Kaup-Newell-Segur equation (AKNSE), have been scrutinized. Bifurcation analysis, sensitivity as well as
M. Akher Chowdhury, M. Mamun Miah, Md Mamunur Rasid, Sadique Rehman, J.R.M. Borhan, Abdul-Majid Wazwaz, Mohammad Kanan   +6 more
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On sl(N) and sl(M|N) integrable open spin chains

, 2004
We study open spin chains based on rational sl(N) and sl(M|N) R-matrices. We classify the solutions of the reflection equations, for both the soliton-preserving and soliton-non-preserving cases.
Arnaudon, D., Avan, J., Crampe', N., Doikou, A., Frappat, L., Ragoucy, E.   +5 more
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