Results 21 to 30 of about 88 (42)
Variational existence theory for hydroelastic solitary waves [PDF]
C. R. Acad. Sci. Paris, Ser. I 354 (2016) 1078-1086, 2016 This paper presents an existence theory for solitary waves at the interface between a thin ice sheet (modelled using the Cosserat theory of hyperelastic shells) and an ideal fluid (of finite depth and in irrotational motion) for sufficiently large values of a dimensionless parameter $\gamma$. We establish the existence of a minimiser of the wave energy
arxiv +1 more source
Stability of ground states for logarithmic Schrödinger equation with a $δ^{\prime}$-interaction [PDF]
Evolution Equations and Control Theory (EECT), Pages: 155 - 175,
Volume 6, Issue 2, June 2017, 2016 In this paper we study the one-dimensional logarithmic Schr\"odinger equation perturbed by an attractive $\delta^{\prime}$-interaction \[ i\partial_{t}u+\partial^{2}_{x}u+ \gamma\delta^{\prime}(x)u+u\, \mbox{Log}\left|u\right|^{2}=0, \quad (x,t)\in\mathbb{R}\times\mathbb{R}, \] where $\gamma>0$.
arxiv +1 more source
A note on the stability for Kawahara-KdV type equations [PDF]
arXiv, 2007 In this paper we establish the nonlinear stability of solitary traveling-wave solutions for the Kawahara-KdV equation $$u_t+uu_x+u_{xxx}-\gamma_1 u_{xxxxx}=0,$$ and the modified Kawahara-KdV equation $$u_t+3u^2u_x+u_{xxx}-\gamma_2 u_{xxxxx}=0,$$ where $\gamma_i\in\mathbb{R}$ is a positive number when $i=1,2$.
arxiv
A new two-component system modelling shallow-water waves [PDF]
arXiv, 2013 For propagation of surface shallow-water waves on irrotational flows, we derive a new two-component system. The system is obtained by a variational approach in the Lagrangian formalism. The system has a non-canonical Hamiltonian formulation. We also find its exact solitary-wave solutions.
arxiv
Stability of standing waves for logarithmic Schrödinger equation with attractive delta potential [PDF]
arXiv, 2016 We consider the one-dimensional logarithmic Schr\"odinger equation with a delta potential. Global well-posedness is verified for the Cauchy problem in H1(R) and in an appropriate Orlicz space. In the attractive case, we prove orbital stability of the ground states via variational approach.
arxiv
Existence of solitary waves solutions for internal waves in two-layers systems [PDF]
arXiv, 2018 The aim of this paper is to establish the existence of solitary wave solutions for two classes of two-layers systems modeling the propagation of internal waves. More precisely we will consider the Boussinesq-Full dispersion system and the Intermediate Long Wave (ILW) system together with its Benjamin-Ono (BO) limit.
arxiv
Modelling surface waves on shear current with quadratic depth-dependence [PDF]
Wave Motion 129 (2024) 103343The currents in the ocean have a serious impact on ocean dynamics, since they affect the transport of mass and thus the distribution of salinity, nutrients and pollutants. In many physically important situations the current depends quadratic-ally on the depth.
arxiv +1 more source
Global bifurcation for the Whitham equation [PDF]
arXiv, 2013 We prove the existence of a global bifurcation branch of $2\pi$-periodic, smooth, traveling-wave solutions of the Whitham equation. It is shown that any subset of solutions in the global branch contains a sequence which converges uniformly to some solution of H\"older class $C^{\alpha}$, $\alpha < \frac{1}{2}$.
arxiv
Numerical generation of periodic traveling wave solutions of some nonlinear dispersive wave equations [PDF]
arXiv, 2015 Proposed in this paper is a numerical procedure to generate periodic traveling wave solutions of some nonlinear dispersive wave equations. The method is based on a suitable modification of a fixed point algorithm of Petviahvili type and solves several drawbacks of some previous algorithms proposed in the literature.
arxiv
Results in PhysicsThe space–time fractional Landau-Ginzburg-Higgs equation and coupled Boussinesq-Burger equation describe the behavior of nonlinear waves in the tropical and mid-latitude troposphere, exhibiting weak scattering, extended connections, arising from the ...
Anamika Podder +4 more
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