Periodic Structure of Equatorial Envelope Rossby Wave Under Influence of Diabatic Heating

A simple shallow-water model with influence of diabatic heating on aβ-plane is applied to investigate the nonlinear equatorial Rossby waves in a shear flow. By the asymptotic method of multiple scales, the cubic nonlinear Schrodinger (NLS for short) equation with an external heating source is derived for large amplitude equatorial envelope Rossby wave in a shear flow. And then various periodic structures for these equatorial envelope Rossby waves are obtained with the help of Jacobi elliptic functions and elliptic equation. It is shown that phase-locked diabatic heating plays an important role in periodic structures of rational form.     

Structures of Equatorial Envelope Rossby Wave Under a Generalized External Forcing

The cubic nonlinear Schrodinger (NLS for short) equation with a generalized external heating source is derived for large amplitude equatorial envelope Rossby wave in a shear flow. And then various periodic structures for these equatorial envelope Rossby waves are obtained with the help of a new transformation, Jacobi elliptic functions,and elliptic equation. It is shown that different types of resonant phase-locked diabatic heating play different roles in structures of equatorial envelope Rossby wave.     

Periodic Structures of Rossby Wave under Influence of Dissipation

A simple barotropic potential vorticity equation with the influence of dissipation is applied to investigate the nonlinear Rossby wave in a shear flow in the tropical atmophere. By the reduetive perturbation method, we derive the rotational KdV （rKdV for short） equation. And then, with the help of Jaeobi elliptie functions, we obtain various periodic structures for these Rossby waves. It is shown that dissipation is very important for these periodic structures of rational form.     

Equatorial Rossby Solitary Wave Under the External Forcing

A simple shallow-water model with influence of external forcing on a β-plane is applied to investigate the nonlinear equatorial Rossby waves in a shear flow. By the perturbation method, the extended variable-coefficient KdV equation under an external forcing is derived for large amplitude equatorial Rossby wave in a shear flow. And then various periodic-like structures for these equatorial Rossby waves are obtained with the help of Jacobi elliptic functions. It is shown that the external forcing plays an important role in various periodic-like structures.     

Envelope Periodic Solutions to Coupled Nonlinear Equations

The envelope periodic solutions to some nonlinear coupled equations are obtained by means of the Jacobielliptic function expansion method. And these envelope periodic solutions obtained by this method can degenerate tothe envelope shock wave solutions and/or the envelope solitary wave solutions.     

Solving Nonlinear Wave Equations by Elliptic Equation

The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions,periodic wave solutions and so on, so it can be taken as a generalized method.     

Elliptic Equation and Its Direct Applications to Nonlinear Wave Equations

Elliptic equation is taken as an ansatz and applied to solve nonlinear wave equations directly. More kinds of solutions are directly obtained, such as rational solutions, solitary wave solutions, periodic wave solutions and so on. It is shown that this method is more powerful in giving more kinds of solutions, so it can be taken as a generalized method.     

Periodic Solutions for Two Coupled Nonlinear-Partial Differential Equations

In this paper, by applying the Jacobi elliptic function expansion method, the periodic solutions for two coupled nonlinear partial differential equations are obtained.     

Periodic Solutions for Two Coupled Nonlinear-Partial Differential Equations

In this paper, by applying the Jacobi elliptic function expansion method, the periodic solutions for two coupled nonlinear partial differential equations are obtained.     

Elliptic Equation and New Solutions to Nonlinear Wave Equations

The new solutions to elliptic equation are shown, and then the elliptic equation is taken as a transformationand is applied to solve nonlinear wave equations. It is shown that more kinds of solutions are derived, such as periodicsolutions of rational form, solitary wave solutions of rational form, and so on.     

Envelope Periodic Solutions to One-Dimensional Gross-Pitaevskii Equation in Bose-Einstein Condensation

In this paper, applying the dependent and independent variables transformations as well as the Jacobi elliptic function expansion method, the envelope periodic solutions to one-dimensional Gross-Pitaevskii equation in Bose-Einstein condensates are obtained.     

New Periodic Wave Solutions, Localized Excitations and Their Interaction Properties for （3＋1）-Dimensional Jimbo-Miwa Equation

Based on the multi-linear variable separation approach, a class of exact, doubly periodic wave solutions for the （3＋1）-dimensional Jimbo-Miwa equation is analytically obtained by choosing the Jacobi elliptic functions and their combinations. Limit cases are considered and some new solitary structures （new dromions） are derived. The interaction properties of periodic waves are numerically studied and found to be inelastic. Under long wave limit, two sets of new solution structures （dromions） are given. The interaction properties of these solutions reveal that some of them are completely elastic and some are inelastic.     

Elliptic Equation and New Solutions to Nonlinear Wave Equations

The new solutions to elliptic equation are shown, and then the elliptic: equation is taken as a transformation and is applied to solve nonlinear wave equations. It is shown that more kinds of solutions are derived, such as periodic solutions of rational form, solitary wave solutions of rational form, and so on.     

立方非线性Schr?dinger方程的Jacobi椭圆函数周期解

本文利用F-展开法,求出了立方非线性Schrodinger方程的由Jacobi椭圆函数表示的行波解;并且在极限情况下,得到了方程的孤波解.     

The Periodic Wave Solutions for Two Nonlinear Evolution Equations

By using the F-expansion method proposed recently, the periodic wave solutions expressed by Jacobi elliptic functions for two nonlinear evolution equations are derived. In the limit cases, the solitary wave solutions and the other type of traveling wave solutions for the system are obtained.     

New Rational Form Solutions to Coupled Nonlinear Wave Equations

The new rational form solutions to the elliptic equation are shown, and then these solutions to the elliptic equation are taken as a transformation and applied to solve nonlinear coupled wave equations. It is shown that more novel kinds of solutions are derived, such as periodic solutions of rational form, solitary wave solutions of rational form,and so on.     

New Rational Form Solutions to Coupled Nonlinear Wave Equations

The new rational form solutions to the elliptic equation are shown, and then these solutions to the elliptic equation are taken as a transformation and applied to solve nonlinear coupled wave equations. It is shown that more novel kinds of solutions are derived, such as periodic solutions of rational form, solitary wave solutions of rational form,and so on.     

Davey-Stewartson方程组的包络周期解和孤立波解

应用Jacobi椭圆函数展开法,求得了Davey-Stewartson方程组的包络周期解和孤立波解． 关键词： Davey-Stewartson方程 Jacobi椭圆函数 包络周期解 孤立波解     

Envelope Periodic Solutions to Bose-Einstein Condensation in Linear Magnetic Field and Time-Dependent Laser Field

In this paper, by applying the extended 3acobi elliptic function expansion method, the envelope periodic solutions and corresponding dark soliton solution, bright soliton solution to Bose-Einstein condensation in linear magnetic field and time-dependent laser field are obtained.     

A New Approach to Solve Nonlinear Wave Equations

From the nonlinear sine-Gordon equation, new transformations are obtained in this paper, which are applied to propose a new approach to construct exact periodic solutions to nonlinear wave equations. It is shown that more new periodic solutions can be obtained by this new approach, and more shock wave solutions or solitary wave solutions can be got under their limit conditions.