Study on Atmospheric Travelling Wave Solutions and Review of Its Present Developments

The scientific achievements of travelling waves in a barotropic atmosphere are introduced, including i) the exist-ence conditions of periodic solutions (wavetrain solutions) and solitary wave solutions (pulse solutions), together with the solution finding methods and a series of related problems, ii) seeking solutions of monotonous wave (wave front) and of nonmonotonous travelling wave (oscillatory wave) by using phase plane shooting technique and iii) progress in the study of travelling wave solution at home and abroad. The investigation of travelling wave solutions in recent years has been found in mathematics, physics, chemistry, biology and other sciences. Over the past decade the prob-lem has been the subject of much interest and become an important area of research. So it is no doubt of great signifi-cance to investigate the travelling wave solutions and thereby explain phenomena of weather.