The problem of tsunami wave generation by variable meteo-conditions is discussed. The simplified linear and nonlinear shallow water models are derived, and their analytical solutions for a basin of constant depth are discussed. The shallow-water model describes well the properties of the generated tsunami waves for all regimes, except the resonance case. The nonlinear-dispersive model based on ...

We prove existence and stability results for a two-parameter family of solitary-wave solutions to a system in which an equation of nonlinear Schrödinger type is coupled to an equation of Korteweg-de Vries type. Such systems model interactions between short and long dispersive waves. The results extend earlier results of Angulo, Albert and Angulo, and Chen. Our proof involves the characterizatio...

We investigate dispersive estimates for the two dimensional Dirac equation with a potential. In particular, we show that the Dirac evolution satisfies a t−1 decay rate as an operator from the Hardy space H to BMO, the space of functions of bounded mean oscillation. This estimate, along with the L conservation law allows one to deduce a family of Strichartz estimates. We classify the structure o...

In this paper, we consider two types of traveling wave systems the generalized Kundu-Mukherjee-Naskar equation. Firstly, due to integrity, obtain their energy functions. Then, dynamical system method is applied study bifurcation behaviours corresponding global phase portraits in different parameter sets. According them, every bounded and unbounded orbits can be identified clearly investigated c...

Abstract The main purpose of this work is solving a generalized (2 + 1)-dimensional nonlinear wave equation via $$\bar{\partial }$$ ∂ ¯ -dressing method. key to process establish connection between characteristic functions and -problem. With use...

The homogeneous balance method can be used to construct exact traveling wave solutions of nonlinear partial differential equations. In this paper, this method is used to construct new soliton solutions of the (3+1) Jimbo--Miwa equation.