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General projective Riccati equation method and exact solutions for generalized KdV-type and KdV–Burgers-type equations with nonlinear terms of any order

✍ Scribed by Yong Chen; Biao Li

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
112 KB
Volume
19
Category
Article
ISSN
0960-0779

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✦ Synopsis

Applying the improved generalized method, which is a direct and unified algebraic method for constructing multiple travelling wave solutions of nonlinear partial differential equations and implemented in a computer algebraic system, we consider the KdV-type equations and KdV-Burgers-type equations with nonlinear terms of any order. As a result, we can not only successfully recover the previously known travelling wave solutions found by existing various tanh methods and other sophisticated methods, but also obtain some new formal solutions. The solutions obtained include kink-shaped solitons, bell-shaped solitons, singular solitons and periodic solutions.

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