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It is known that there are nonlinear wave equations with localized solitary wave solutions. Some of these solitary waves are stable (with respect to a small perturbation of initial data) and have nonzero spin (nonzero intrinsic angular…

Pattern Formation and Solitons · Physics 2009-11-13 Q. E. Hoq

We consider a system of NLS with cubic interactions arising in nonlinear optics without Galilean symmetry. The absence of Galilean symmetry can lead to many difficulties, such as global existence and blowup problems; see [Comm. Partial…

Analysis of PDEs · Mathematics 2024-08-06 Yuan Li , Kai Wang , Qingxuan Wang

The nolinear hydrodynamic equations of the surface of a liquid drop are shown to be directly connected to Korteweg de Vries (KdV, MKdV) systems, giving traveling solutions that are cnoidal waves. They generate multiscale patterns ranging…

Fluid Dynamics · Physics 2009-11-06 Andrei Ludu , Jerry P. Draayer

We present a phenomenological approach to dispersion in nonlinear elasticity. A simple, thermomechanically sound, constitutive model is proposed to describe the (non-dissipative) properties of a hyperelastic dispersive solid, without…

Soft Condensed Matter · Physics 2013-03-12 Michel Destrade , Giuseppe Saccomandi

We study the existence of cylindrically symmetric electro-magneto-static solitary waves for a system of a nonlinear Klein-Gordon equation coupled with Maxwell's equations in presence of a positive mass and of a nonnegative nonlinear…

Analysis of PDEs · Mathematics 2015-04-10 Dimitri Mugnai , Matteo Rinaldi

We establish several existence results for traveling-wave solutions of the nonlocal derivative nonlinear Schr\"odinger equation with general coefficients by variational methods. We study associated minimization problems in the subcritical…

Analysis of PDEs · Mathematics 2026-04-10 Amin Esfahani , Adilbek Kairzhan , Mukhtar Karazym

We are interested to the existence of standing waves for the nonlinear Klein Gordon equation {\epsilon}^2{\box}{\psi} + W'({\psi}) = 0 in a bounded domain D. The main result of this paper is that, under suitable growth condition on W, for…

Analysis of PDEs · Mathematics 2010-12-30 Marco G. Ghimenti , Carlo R. Grisanti

The covariant Klein-Gordon equation requires twice the boundary conditions of the Schrodinger equation and does not have an accepted single-particle interpretation. Instead of interpreting its solution as a probability wave determined by an…

Quantum Physics · Physics 2014-11-18 K. B. Wharton

We study the equation $u_t +uu_x +u-K*u=0$ in the case of an arbitrary $K \geq 0$, which is a generalization of a model for radiating gas, in which $K(y)={1/2}e^{-|y|}$. Using a monotone iteration scheme argument we establish the existence…

Mathematical Physics · Physics 2007-05-23 Adam Chmaj

In this paper we study global nonlinear stability for a system of semilinear wave and Klein-Gordon equations with quadratic nonlinearities. We consider nonlinearities of the type of wave-Klein-Gordon interactions where there are no…

Analysis of PDEs · Mathematics 2023-03-14 Qian Zhang

In this paper, we study local well-posedness and orbital stability of standing waves for a singularly perturbed one-dimensional nonlinear Klein-Gordon equation. We first establish local well-posedness of the Cauchy problem by a fixed point…

Analysis of PDEs · Mathematics 2019-11-12 Elek Csobo , François Genoud , Masahito Ohta , Julien Royer

We prove the existence of bound and ground states for a system of coupled nonlinear Schr\"odinger-Korteweg-de Vries equations, depending on the size of the coupling coefficient.

Classical Analysis and ODEs · Mathematics 2014-11-25 Eduardo Colorado

This paper sheds new light on the stability properties of solitary wave solutions associated with models of Korteweg-de Vries and Benjamin\&Bona\&Mahoney type, when the dispersion is very lower. Via an approach of compactness, analyticity…

Analysis of PDEs · Mathematics 2018-03-14 Jaime Angulo Pava

We prove the existence of a continuous family of positive and generally non-monotone travelling fronts in delayed reaction-diffusion equations $u_t(t,x) = \Delta u(t,x)- u(t,x) + g(u(t-h,x)) (*)$, when $g \in C^2(R_+,R_+)$ has exactly two…

Dynamical Systems · Mathematics 2013-03-04 Teresa Faria , Sergei Trofimchuk

We consider the nonlinear Schr{\"o}dinger equation with a harmonic potential in the presence of two combined energy-subcritical power nonlinearities. We assume that the larger power is defocusing, and the smaller power is focusing. Such a…

Analysis of PDEs · Mathematics 2025-07-23 Rémi Carles , Yavdat Ilyasov

We consider a damped, parametrically driven discrete nonlinear Klein-Gordon equation, that models coupled pendula and micromechanical arrays, among others. To study the equation, one usually uses a small-amplitude wave ansatz, that reduces…

Pattern Formation and Solitons · Physics 2019-11-21 Y. Muda , F. T. Akbar , R. Kusdiantara , B. E. Gunara , H. Susanto

We study the stability of standing-waves solutions to a scalar non-linear Klein-Gordon equation in dimension one with a quadratic-cubic non-linearity. Orbits are obtained by applying the semigroup generated by the negative complex unit…

Analysis of PDEs · Mathematics 2022-09-12 Daniele Garrisi

We prove the existence of normalized ground state solutions for the biharmonic Schr\"odinger equation with combined nonlinearities and show that all ground states correspond to the local minima of the associated energy functional restricted…

Analysis of PDEs · Mathematics 2023-05-02 Xiaojun Chang , Hichem Hajaiej , Zhouji Ma , Linjie Song

This paper establishes the global existence of solutions for a class of wave-Klein-Gordon coupled systems with specific nonlinearities in 3+1-dimensional Minkowski spacetime. The study demonstrates that imposing certain constraints on the…

Analysis of PDEs · Mathematics 2026-04-21 Yue Ma , Weidong Zhang

In the present work we explore the competition of quadratic and quartic dispersion in producing kink-like solitary waves in a model of the nonlinear Schr{\"o}dinger type bearing cubic nonlinearity. We present the first 6 families of…

Pattern Formation and Solitons · Physics 2023-08-09 G. A. Tsolias , Robert J. Decker , A. Demirkaya , T. J. Alexander , Ross Parker , P. G. Kevrekidis