# Line-solitons, line-shocks, and conservation laws of a universal KP-like equation in 2+1 dimensions

## TL;DR

This paper investigates a universal KP-like equation in 2+1 dimensions, deriving conservation laws and explicit line-soliton solutions, revealing significant differences from classical KP solitons and identifying a line-shock phenomenon.

## Contribution

It derives all low-order conservation laws and explicitly constructs all line-soliton solutions for a universal KP-like equation, highlighting novel properties and a line-shock solution.

## Key findings

- Derived conservation laws including momenta, energy, and topological charges.
- Explicitly obtained all line-soliton solutions with parameterization.
- Identified a line-shock solution as a limiting case.

## Abstract

A universal KP-like equation in 2+1 dimensions, which models general nonlinear wave phenomena exhibiting p-power nonlinearity, dispersion, and small transversality, is studied. Special cases include the integrable KP (Kadomtsev-Petviashvili) equation and it is modified version, as well as their p-power generalizations. Two main results are obtained. First, all low-order conservation laws are derived, including ones that arise for special powers p. The conservation laws comprise momenta, energy, and Galilean-type quantities, as well as topological charges. Their physical meaning and properties are discussed. Second, all line-soliton solutions are obtained in an explicit form. A parameterization is given using the speed and the direction angle of the line-soliton, and the allowed kinematic region is determined in terms of these parameters. Basic kinematical properties of the line-solitons are also discussed. These properties differ significantly compared to those for KP line-solitons and their p-power generalizations. A line-shock solution is shown to emerge when a special limiting case of the kinematic region is considered.