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Periodic Wave Solutions and Their Limit Forms for A mKdV Equation

Author: YeHaiYa（Yahia Badawi Bashir Meny）
Tutor: LiuZhengRong
School: South China University of Technology
Course: Applied Mathematics
Keywords: mKdV equation Branch method Trigonometric functions periodic wave solutions Elliptic function periodic wave solutions Limiting form
CLC: O175
Type: Master's thesis
Year: 2011
Downloads: 15
Quote: 0
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Abstract


MKdV equation using the qualitative theory of differential equations of this study are as follows , the branch method , integration method and numerical simulation, periodic wave solutions of the above equation and its limit , and obtained the following results (1 °) in the wave velocity is greater than zero, in the the zero two conditions , respectively, in the parameter a? b plane is determined to be out of eight branches of the rays, a - b plane is divided into eight regions . (2 ° ) in eight branch ray and 8 regions , determine the the branch phase diagram of the traveling wave system . (3 °) proved the special boundaries closed trajectory in the phase diagram and determine the the special boundaries closed trajectory parameters area and its precise location of the phase diagram . (4 °) to take advantage of special boundaries closed trajectory , the wave solutions of the equation existence posed by a trigonometric cycle . (5 °) to the of special boundaries closed orbit homoclinic orbits for the line, the periodic orbit classification respectively rail departure from a variety of cycle , derive the equation of three types of elliptic function periodic wave solutions . (6 °) for various directions of the three types of elliptic function periodic wave solutions limit the study , which also derive a triangular function periodic wave solutions , and also get a solitary wave solutions .

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations
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