Results 1 to 10 of about 55 (54)

Multi-solitons for nonlinear Klein–Gordon equations

Forum of Mathematics, Sigma, 2014
In this paper, we consider the existence of multi-soliton structures for the nonlinear Klein–Gordon (NLKG) equation in $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\
RAPHAËL CÔTE, CLAUDIO MUÑOZ
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Existence and evenness of solitary-wave solutions for an equation of short and long dispersive waves

, 2015
We study the existence and some properties of solitary-wave solutions for an interaction equation between a long internal wave and a short surface wave in a two-layer fluid.
Angulo, J, Montenegro, JF
core   +1 more source

Ground state solutions to singularly perturbed Chern-Simons-Schrödinger systems with a neutral scalar field

Demonstratio Mathematica
In this paper, we consider the following singularly perturbed Chern-Simons-Schrödinger systems(P) −ε2Δu+e2|A|2+V(x)+2eA0+21+κq2Nu+q|u|p−2u=0, −ε2ΔN+κ2q2N+q1+κq2u2=0, εκ∂1A2−∂2A1=−eu2,∂1A1+∂2A2=0, εκ∂1A0=e2A2u2,εκ∂2A0=−e2A1u2, $$\begin{cases}\quad \hfill &
Deng Jin
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Lie point symmetry, conservation laws and exact power series solutions to the Fujimoto-Watanabe equation

, 2021
In this paper, the Fujimoto-Watanabe equation is studied with the help of the classical Lie point symmetry analysis method. Infinitesimal generators, the entire geometric vector fields and symmetry groups of the Fujimoto-Watanabe equation are given.
Liu, Yu, Dong, Huanhe, Guo, Baoyong, Fang, Yong   +3 more
core  

The initial-value problem for a Gardner-type equation

Advanced Nonlinear Studies
Discussed here is a regularized version(0.1)ut+ux+uux+Au2ux−uxxt=0, $${u}_{t}+{u}_{x}+u{u}_{x}+A{u}^{2}{u}_{x}-{u}_{\mathit{xxt}}=0,$$ of the classical Gardner equationut+ux+uux+Au2ux+uxxx=0, $${u}_{t}+{u}_{x}+u{u}_{x}+A{u}^{2}{u}_{x}+{u}_{\mathit{xxx ...
Bona Jerry, Chen Hongqiu, Guerrero Pamela, Haidau Cristina, Pantic Sanja   +4 more
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On the 3-Wave Equations with Constant Boundary Conditions [PDF]

, 2012
2010 Mathematics Subject Classification: 37K40, 35Q15, 35Q51, 37K15.The inverse scattering transform for a special case of the 3- wave resonant interaction equations with non-vanishing boundary conditions is studied.
Gerdjikov, V. S., Grahovski, G. G.
core  

Local well-posedness for the two-component Benjamin-Ono equation

Advances in Nonlinear Analysis
The Cauchy problem for the two-component Benjamin-Ono equation is considered. It is shown that this problem is local well-posed in Hs(R)×Hs(R){H}^{s}\left({\mathbb{R}})\times {H}^{s}\left({\mathbb{R}}) for any s>9⁄8s\gt 9/8.
Zhao Min
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On the Transformations of Symplectic Expansions and the Respective Bäcklund Transformation for the KDV Equation [PDF]

, 2003
2000 Mathematics Subject Classification: Primary: 34B40; secondary: 35Q51, 35Q53By using the Deift–Trubowitz transformations for adding or removing bound states to the spectrum of the Schrödinger operator on the line we construct a simple algorithm ...
Khristov, E.
core  

Genus two KdV soliton gases and their long-time asymptotics

Forum of Mathematics, Sigma
This paper employs the Riemann-Hilbert problem and nonlinear steepest descent method of Deift-Zhou to provide a comprehensive analysis of the asymptotic behavior of the genus two Korteweg-de Vries soliton gases.
Deng-Shan Wang, Dinghao Zhu, Xiaodong Zhu   +2 more
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Chaotic and quasi-periodic dynamics in nonlinear micro-strain wave systems: Exact symbolic solutions and symmetry-based analysis

Results in Engineering
This work presents a systematic theoretical and computational investigation of the micro-strain wave (MSW) model, a fundamental nonlinear evolution equation governing propagation phenomena in media with microscale deformation effects.
Mostafa M.A. Khater
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