Abstract
Publisher Summary This chapter discusses solitary wave solutions of generalized Korteweg-de Vries (KdV) equations. The chapter begins with a discussion of the existence of solitary wave solutions of the scalar Korteweg-deVries (KdV) and modified Korteweg-de Vries equations, including the derivation of formulas for wave amplitude and speed when the waves move against a nonzero “background.” This is followed by a consideration of related questions for system analogs of (KdV). The approach involves the consistent use of the asymptotic theory of second-order singularly perturbed boundary value problems, and hence it offers a convenient alternative to more traditional analytical and numerical methods. The solitary waves in each component evolve independently of each other.
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