Related papers: A uniqueness result for the two vortex travelling …
This paper deals with the existence of travelling wave solutions for a general one-dimensional nonlinear Schr\"odinger equation. We construct these solutions by minimizing the energy under the constraint of fixed momentum. We also prove…
We investigate the existence and properties of traveling waves for the Euler-Korteweg system with general capillarity and pressure. Our main result is the existence in dimension two of waves with arbitrarily small energy. They are obtained…
We prove the existence of nontrivial finite energy traveling waves for a large class of nonlinear Schr\"odinger equations with nonzero conditions at infinity (includindg the Gross-Pitaevskii and the so-called "cubic-quintic" equations) in…
We consider the nonlinear Schr\"odinger equation with nonzero conditions at infinity in $\R^2$. We investigate the existence of traveling waves that are periodic in the direction transverse to the direction of propagation and minimize the…
We look for traveling wave solutions to the nonlinear Schr\"odinger equation with a subsonic speed, covering several physical models with Sobolev subcritical nonlinear effects. Our approach is based on a variant of Sobolev-type inequality…
The nonlinear Schroedinger equation has several families of quasi-periodic travelling waves, each of which can be parametrized up to symmetries by two real numbers: the period of the modulus of the wave profile, and the variation of its…
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…
For the one-dimensional mass-critical/supercritical pseudo-relativistic nonlinear Schrodinger equation, a stationary solution can be constructed as an energy minimizer under an additional kinetic energy constraint and the set of energy…
In this paper, we continue the study of the dynamics of the traveling waves for nonlinear Schr\"odinger equation with derivative (DNLS) in the energy space. Under some technical assumptions on the speed of each traveling wave, the stability…
We study the stability of traveling waves of nonlinear Schr\"odinger equation with nonzero condition at infinity obtained via a constrained variational approach. Two important physical models are Gross-Pitaevskii (GP) equation and…
In this paper, we systematically study the existence, asymptotic behaviors, uniqueness, and nonlinear orbital stability of traveling-wave solutions with small propagation speeds for the generalized surface quasi-geostrophic (gSQG) equation.…
As a sequel to our previous analysis in [9] arXiv:2202.09411 on the Gross-Pitaevskii equation on the product space $\mathbb{R} \times \mathbb{T}$, we construct a branch of finite energy travelling waves as minimizers of the Ginzburg-Landau…
We consider the problem of existence and stability of solitary traveling waves for the one dimensional discrete non linear Schroedinger equation (DNLS) with cubic nonlinearity, near the continuous limit.We construct a family of solutions…
The existence of nonzero periodic travelling wave solutions for a general discrete nonlinear Schr\"odinger equation (DNLS) on finite one-dimensional lattices is proved. The DNLS features a general nonlinear term and variable range of…
The nonlinear Schroedinger equation possesses three distinct six-parameter families of complex-valued quasi-periodic travelling waves, one in the defocusing case and two in the focusing case. All these solutions have the property that their…
For a large class of nonlinear Schr\"odinger equations with nonzero conditions at infinity and for any speed $c$ less than the sound velocity, we prove the existence of nontrivial finite energy traveling waves moving with speed $c$ in any…
For a nonlinear Schr\"odinger system with mass critical exponent, we prove the existence and orbital stability of standing-wave solutions obtained as minimizers of the underlying energy functional restricted to a double mass constraint. In…
This article is concerned with the mathematical analysis of a class of a nonlinear fractional Schrodinger equations with a general Hartree-type integrand. We prove existence and uniqueness of global-in-time solutions to the associated…
In the work of Colliander et al. (2010), a minimal lattice model was constructed describing the transfer of energy to high frequencies in the defocusing nonlinear Schr\"odinger equation. In the present work, we present a systematic study of…
We present an existence and stability theory for gravity-capillary solitary waves with constant vorticity on the surface of a body of water of finite depth. Exploiting a rotational version of the classical variational principle, we prove…