scholarly journals A Newton-Type Approach to Approximate Travelling Wave Solutions of a Schrödinger-Benjamin-Ono System

2018 ◽  
Vol 2018 ◽  
pp. 1-17
Author(s):  
Juan Carlos Muñoz Grajales
Keyword(s):  
Iterative Method ◽  
Solitary Waves ◽  
Numerical Scheme ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Newton’S Iterative Method ◽  
Wave Solutions

We introduce a Newton’s iterative method to approximate periodic and nonperiodic travelling wave solutions of the Schrödinger-Benjamin-Ono system derived by M. Funakoshi and M. Oikawa. We analyze numerically the influence of the model’s parameters on these solutions and illustrate the collision of two unequal-amplitude solitary waves propagating with different speeds computed by using the proposed numerical scheme.

scholarly journals Asymmetric gravity–capillary solitary waves on deep water

2014 ◽  
Vol 759 ◽  
Author(s):  
Z. Wang ◽  
J.-M. Vanden-Broeck ◽  
P. A. Milewski
Keyword(s):  
Wave Propagation ◽  
Solitary Waves ◽  
Travelling Wave ◽  
Propagation Direction ◽  
Travelling Wave Solutions ◽  
Two Dimensional ◽  
Bifurcation Curve ◽  
Wave Propagation Direction ◽  
Wave Solutions ◽  
Deep Fluid

AbstractWe present new families of gravity–capillary solitary waves propagating on the surface of a two-dimensional deep fluid. These spatially localised travelling-wave solutions are non-symmetric in the wave propagation direction. Our computation reveals that these waves appear from a spontaneous symmetry-breaking bifurcation, and connect two branches of multi-packet symmetric solitary waves. The speed–energy bifurcation curve of asymmetric solitary waves features a zigzag behaviour with one or more turning points.

scholarly journals Error Analysis of an Implicit Spectral Scheme Applied to the Schrödinger-Benjamin-Ono System

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Juan Carlos Muñoz Grajales
Keyword(s):  
Gravity Waves ◽  
Numerical Scheme ◽  
Water Regime ◽  
Approximate Solutions ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Fully Discrete ◽  
Two Fluids ◽  
Wave Solutions ◽  
Numerical Solver

We develop error estimates of the semidiscrete and fully discrete formulations of a Fourier-Galerkin numerical scheme to approximate solutions of a coupled nonlinear Schrödinger-Benjamin-Ono system that describes the motion of two fluids with different densities under capillary-gravity waves in a deep water regime. The accuracy of the numerical solver is checked using some exact travelling wave solutions of the system.

Nonlinear Partial Differential Equations Solved by Projective Riccati Equations Ansatz

2003 ◽  
Vol 58 (9-10) ◽  
pp. 511-519 ◽  
Author(s):  
Biao Li ◽  
Yong Chen
Keyword(s):  
Solitary Waves ◽  
Boussinesq Equation ◽  
Nonlinear Partial Differential Equations ◽  
Riccati Equations ◽  
Travelling Wave ◽  
Reaction Diffusion Equation ◽  
Travelling Wave Solutions ◽  
Rational Solutions ◽  
Wave Solutions ◽  
Nonlinear Reaction Diffusion Equation

Based on the general projective Riccati equations method and symbolic computation, some new exact travelling wave solutions are obtained for a nonlinear reaction-diffusion equation, the highorder modified Boussinesq equation and the variant Boussinesq equation. The obtained solutions contain solitary waves, singular solitary waves, periodic and rational solutions. From our results, we can not only recover the known solitary wave solutions of these equations found by existing various tanh methods and other sophisticated methods, but also obtain some new and more general travelling wave solutions.

Solitary and Travelling Wave Solutions of Certain Nonlinear Diffusion-Reaction Equations

2020 ◽  
Author(s):  
Miftachul Hadi
Keyword(s):  
Nonlinear Diffusion ◽  
Travelling Wave ◽  
Diffusion Reaction ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Reaction Equations

We review the work of Ranjit Kumar, R S Kaushal, Awadhesh Prasad. The work is still in progress.

scholarly journals Singularity analysis and analytic solutions for the Benney–Gjevik equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Andronikos Paliathanasis ◽  
Genly Leon ◽  
P. G. L. Leach
Keyword(s):  
Evolution Equations ◽  
Singularity Analysis ◽  
Analytic Solutions ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Painlevé Test ◽  
Wave Solutions ◽  
Algebraic Solutions

Abstract We apply the Painlevé test for the Benney and the Benney–Gjevik equations, which describe waves in falling liquids. We prove that these two nonlinear 1 + 1 evolution equations pass the singularity test for the travelling-wave solutions. The algebraic solutions in terms of Laurent expansions are presented.

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