Long‐time asymptotics of non‐decaying solutions of the $(2+1)$ ‐dimensional Gardner equation

Abstract

We prove the existence of non‐decaying real solutions of the $(2+1)$ ‐dimensional Gardner equation, vanishing when $x\to +\infty$ . We give asymptotic formulae for the solutions in terms of infinite series of asymptotic solitons with curved lines of constant phase and varying amplitude for $\vert t\vert \to\infty$ .