INFINITELY MANY SOLITARY WAVES DUE TO THE SECOND-HARMONIC GENERATION IN QUADRATIC MEDIA

doi:10.1007/s10473-020-0102-3

Abstract

Abstract:

In this paper, we consider the following coupled Schr?dinger system with χ⁽²⁾ nonlinearities

which arises from second-harmonic generation in quadratic media. Here V₁(x) and V₂(x) are radially positive functions, 2 ≤ N < 6, α > 0 and α > β. Assume that the potential functions V₁(x) and V2(x) satisfy some algebraic decay at infinity. Applying the finite dimensional reduction method, we construct an unbounded sequence of non-radial vector solutions of synchronized type.

Key words: χ⁽²⁾ nonlinearities, second-harmonic generation, synchronized solution, reduction method

CLC Number:

35J10

Chunhua WANG, Jing ZHOU. INFINITELY MANY SOLITARY WAVES DUE TO THE SECOND-HARMONIC GENERATION IN QUADRATIC MEDIA[J].Acta mathematica scientia,Series B, 2020, 40(1): 16-34.

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