Shock waves, chiral solitons and semiclassical limit of one-dimensional anyons

Abstract

This paper is devoted to the semiclassical limit of the one-dimensional Schr€ o odinger equation with current nonlinearity and Sobolev regularity, before shocks appear in the limit system. In this limit, the modified Euler equations are recovered. The strictly hyperbolicity and genuine nonlinearity are proved for the limit system wherever the Riemann invariants remain distinct. The dispersionless equation and its deformation which is the quantum potential perturbation of JNLS equation are also derived.

A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo–Miwa equation

“…A similar diversity situation of exact solutions can be found in solution spaces of typical nonlinear wave equations, for instance, the 1 + 1 dimensional equations: the Korteweg-de Vries equation [44,45], the Boussinesq equation [46,47], the nonlinear Schrödinger type equation [48] and the Hirota-Satsuma coupled KdV equation [49], and the 2 + 1 dimensional equations: the Kadomtsev-Petviashvili equation [50], the DaveyStewartson equation [51,52] and the Boiti-Leon-Pempinelli dispersive long-wave system [53].…”

Envelope soliton resonances and broer-kaup-type non-madelung fluids

“…The Madelung fluid representation of the Schrödinger equation is an important tool, first created for interpreting quantum mechanics [1], [2] and then realized as a quantum fluid model [3] and later as a proper tool for describing the semiclassical limit of envelope soliton equations of the nonlinear Schrödinger (NLS) type [4], [5]. Here, we use it to generalize the NLS equation by extending the dispersion term.…”

Резонансы Солитонов Огибающих И Немаделунговы Жидкости Типа Броера - Каупа

“…Представление в виде жидкости Маделунга для уравнения Шредингера является важным инструментом, который впервые был создан для интерпретации кванто-вой механики [1], [2], затем был реализован в виде модели квантовой жидкости [3] и позже использовался как подходящий способ описания квазиклассического преде-ла в солитонных уравнениях огибающих типа нелинейного уравнения Шредингера (НУШ) [4], [5]. В настоящей статье мы используем его для обобщения НУШ, расши-ряя дисперсионный член.…”