Generalizations of the short pulse equation

Abstract

We classify integrable scalar polynomial partial differential equations of second order generalizing the short pulse equation.

References in corpus (12)

• An integrable shallow water equation with peaked solitons
• The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
• The short pulse equation is integrable
• The Bi-Hamiltonian Structure of the Short Pulse Equation
• Nonlinear balance and exchange of stability in dynamics of solitons, peakons, ramps/cliffs and leftons in a 1+1 nonlinear evolutionary pde
• Perturbative Symmetry Approach
• Quantum quenching of radiation losses in short laser pulses
• Integrable and non-integrable equations with peakons
• Transformation and integrability of a generalized short pulse equation
• Integrable semi-discretizations of the reduced Ostrovsky equation
• The Hunter-Saxton equation: remarkable structures of symmetries and conserved densities
• On the $\tau$-functions of the reduced Ostrovsky equation and the $A_2^{(2)}$ two-dimensional Toda system

Cited by in corpus (8)

• Integrability of a generalized short pulse equation revisited
• Parametric solutions of the generalized short pulse equations
• Super Extensions of the Short Pulse Equation
• On the Cauchy problem for the Hunter-Saxton equation on the line
• Integrable negative flows of the Heisenberg ferromagnet equation hierarchy
• On a new avatar of the sine-Gordon equation
• D'Alembert-type solution of the Cauchy problem for a Boussinesq-Klein-Gordon equation
• A note on isometric immersions and differential equations which describe pseudospherical surfaces