A new two-component system modelling shallow-water waves

TL;DR

This paper introduces a novel two-component mathematical model for shallow-water wave propagation, derived via variational methods, with a non-canonical Hamiltonian structure and exact solitary-wave solutions.

Contribution

It presents a new two-component system for shallow-water waves derived through a variational approach, including its Hamiltonian formulation and solitary-wave solutions.

Findings

Derivation of a new two-component shallow-water wave model

Identification of a non-canonical Hamiltonian structure

Exact solitary-wave solutions found

Abstract

For propagation of surface shallow-water waves on irrotational flows, we derive a new two-component system. The system is obtained by a variational approach in the Lagrangian formalism. The system has a non-canonical Hamiltonian formulation. We also find its exact solitary-wave solutions.