Hirota method for oblique solitons in two-dimensional supersonic nonlinear Schroedinger flow

TL;DR

This paper demonstrates that single oblique soliton solutions in 2D nonlinear Schrödinger flow can be formulated using Hirota's bilinear method, and explores the near-integrability of the system for small angles or high velocities.

Contribution

It introduces a Hirota bilinear formalism for oblique solitons and analyzes the conditions under which the system approaches integrability.

Findings

Single soliton solutions expressed via Hirota formalism

Near-integrability for small soliton angles or hypersonic speeds

Two-soliton solutions suggest approximate integrability

Abstract

In a previous work[1] exact stable oblique soliton solutions were revealed in two dimensional nonlinear Schroedinger flow. In this work we show that single soliton solution can be expressed within the Hirota bilinear formalism. An attempt to build two-soliton solutions shows that the system is "close" to integrability provided that the angle between the solitons is small and/or we are in the hypersonic limit.