Symmetry analysis for three-dimensional dissipation Rossby waves

Abstract

Rossby waves, belonging to the most important waves in the atmosphere and ocean, can affect the energy transfer of the atmosphere and ocean and have significant theoretical meaning and research value. In previous research performed with the theory and calculation method limit, the dissipation effect was commonly ignored. However, under the conditions of the weak linear approximation, the magnitude difference between nonlinear and dissipation is small, and the dissipation effect must be considered. In this paper, based on the classic Lie group approach, the (3 + 1)-dimensional quasi-geodetiophic vorticity equation with dissipation effect is solved. With the help of the solutions, we can better comprehend the influence of the dissipation effect on the propagation of Rossby waves.

The Prolongation Structure of the Modified Nonlinear Schrödinger Equation and Its Initial-Boundary Value Problem on the Half Line via the Riemann-Hilbert Approach

“…Many works on nonlinear evolution equations have been studied, such as the Hamiltonian structure [1,2], the infinite conservation laws [3,4], the Bäcklund transformation [5,6] and so on [7][8][9]. Besides, the exact solution of these equations, which can be expressed in various forms by different methods, is also a significant subject of soliton research [10][11][12][13][14][15][16][17][18][19][20][21][22]. In recent years, with the development of soliton theory, more and more researchers pay attention to the Riemann-Hilbert approach.…”

Prolongation Structures and N‐Soliton Solutions for a New Nonlinear Schrödinger‐Type Equation via Riemann‐Hilbert Approach

“…In recent decades, nonlinear partial differential equations (PDEs) play a significant role in mathematics and theoretical physics, which have attracted much attentions in soliton theory and integrable system [1,2]. Since exact solutions [3,4] of the integrable equations [5,6] can describe and explain many natural phenomena [7], the study of integrable equations has become a hot topic. It is well known that inverse scattering transform [8,9] is a very important theory for solving exact solutions of integrable equations.…”

Asymptotic Analysis of Impulsive Dispersal Predator-Prey Systems with Markov Switching on Finite-State Space

“…Takeuchi in [2] established the sufficient conditions for persistence of the single dispersal system and verified the existence and uniqueness of the globally positive equilibrium. Then two species or multiple species dispersal system have been investigated by many authors [3][4][5][6][7]. Kuang et al investigated the relationship between the stability of the population and the dispersal rate of the prey species in [3].…”