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We derive the Whitham modulation equations for the nonlinear Schr\"odinger equation in the plane (2d NLS) with small dispersion. The modulation equations are derived in terms of both physical and Riemann variables; the latter yields…

Pattern Formation and Solitons · Physics 2021-09-21 Mark J. Ablowitz , Justin T. Cole , Igor Rumanov

An outstanding challenge in the field of topological insulators is the realization of nonlinear systems that support coherent traveling waves. Highly nonlinear lattices can suffer from significant radiation losses due to Peierls-Nabarro…

Pattern Formation and Solitons · Physics 2026-04-22 Troy I. Johnson , Justin T. Cole

In this work, we study the Benjamin-Bona-Mahony like equations with a fully nonlinear dispersive term by means of the factorization technique. In this way we find the travelling wave solutions of this equation in terms of the Weierstrass…

Exactly Solvable and Integrable Systems · Physics 2015-05-13 S. Kuru

This paper reports a theoretical and numerical framework to model nonlinear waves in elastic-plastic solids. Formulated in the Eulerian frame, the governing equations employed include the continuity equation, the momentum equation, and an…

Numerical Analysis · Mathematics 2023-03-29 Lixiang Yang , Robert L Lowe

In this note, we study the existence of traveling waves of a surface model in a non-newtonian fluid with odd viscosity. The proof relies on nonlinear bifurcation techniques.

Analysis of PDEs · Mathematics 2024-07-30 Diego Alonso-Orán , Claudia García , Rafael Granero-Belinchón

The purpose of this paper is to prove that, for a large class of nonlinear evolution equations known as scalar viscous balance laws, the spectral (linear) instability condition of periodic traveling wave solutions implies their orbital…

Analysis of PDEs · Mathematics 2022-09-05 Enrique Álvarez , Jaime Angulo Pava , Ramón G. Plaza

The longstanding problem of moving discrete solitary waves in nonlinear Schr{\"o}dinger lattices is revisited. The context is photorefractive crystal lattices with saturable nonlinearity whose grand-canonical energy barrier vanishes for…

Pattern Formation and Solitons · Physics 2015-05-25 T. R. O. Melvin , A. R. Champneys , P. G. Kevrekidis , J. Cuevas

We investigate a new class of topological travelling-wave solutions for a macroscopipc swarmalator model involving force non-reciprocity. Swarmalators are systems of self-propelled particles endowed with a phase variable. The particles are…

Mathematical Physics · Physics 2023-07-28 Pierre Degond , Antoine Diez

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

In this work we derive evolution equations for the nonlinear behavior of a coasting beam under the influence of a resonator impedance. Using a renormalization group approach we find a set of coupled nonlinear equations for the beam density…

Accelerator Physics · Physics 2007-05-23 S. I. Tzenov , P. L. Colestock

We prove the existence of a smooth curve of periodic traveling wave solutions for the Zakharov system. We also show that this type of solutions are nonlinear stable by the periodic flow generated for the system mentioned before. An…

Analysis of PDEs · Mathematics 2010-11-19 Jaime Angulo , Carlos Banquet

We investigate the existence and nonexistence of traveling wave solutions near monotonic shear flows with non-constant background density for the two-dimensional inhomogeneous Euler equations in a finite channel. For any small $\tau>0$,…

Analysis of PDEs · Mathematics 2026-02-03 Qi Zhao , Weiren Zhao

We consider the stability and instability of periodic travling waves for Korteweg-de Vries type equations with fractional dispersion and other nonlinear dispersive equations. We establish that a constrained minimizer for the related…

Analysis of PDEs · Mathematics 2015-01-13 Vera Mikyoung Hur , Mathew A. Johnson

A key feature of $(1+1)$-dimensional nonlinear wave equations is that they admit left or right traveling waves, under appropriate algebraic conditions on the nonlinearities. In this paper, we prove global stability of such traveling wave…

Analysis of PDEs · Mathematics 2023-01-31 Louis Dongbing Cha , Arick Shao

Some classes of the so called "travelling wave" solutions of Einstein and Einstein - Maxwell equations in General Relativity and of dynamical equations for massless bosonic fields in string gravity in four and higher dimensions are…

General Relativity and Quantum Cosmology · Physics 2015-11-13 George Alekseev

We study travelling wave solutions of a generalised Korteweg-de Vries-Burgers equation with a non-local diffusion term and a concave-convex flux. This model equation arises in the analysis of a shallow water flow by performing formal…

Analysis of PDEs · Mathematics 2024-12-05 F. Achleitner , C. M. Cuesta , X. Diez-Izagirre

We prove the orbital stability of periodic traveling-wave solutions for systems of dispersive equations with coupled nonlinear terms. Our method is basically developed under two assumptions: one concerning the spectrum of the linearized…

Analysis of PDEs · Mathematics 2020-02-13 Fabrício Cristófani , Ademir Pastor

The linear stability analysis of an uniform shear flow of granular materials is revisited using several cases of a Navier-Stokes'-level constitutive model in which we incorporate the global equation of states for pressure and thermal…

Soft Condensed Matter · Physics 2008-11-18 Meheboob Alam , Priyanka Shukla , Stefan Luding

We propose a new type of traveling wave pattern, one that can adapt to the size of physical system in which it is embedded. Such a system arises when the initial state has an instability that extends down to zero wavevector, connecting at…

Subcellular Processes · Quantitative Biology 2017-01-04 David A. Kessler , Herbert Levine

An equation to describe nearly one-dimensional traveling-waves patterns is put forward. This is a dispersive generalization of the classical Newell-Whitehead-Segel (NWS) equation. Transverse stability of plane waves is considered within the…

patt-sol · Physics 2008-02-03 Boris Malomed