Higher dimensional solitary waves generated by second-harmonic generation in quadratic media


DOI: 10.1007/s00526-015-0879-1

Cite this article as:
Zhao, L., Zhao, F. & Shi, J. Calc. Var. (2015) 54: 2657. doi:10.1007/s00526-015-0879-1


Schrödinger type soliton waves generated by second-harmonic generation in higher dimensional quadratic optical media are considered. The existence of ground state solutions for spatial dimension from two to five is proved, and the continuous dependence on the parameter and asymptotic behavior of ground state solutions are established. Multi-pulse solutions with certain symmetry are also obtained. In a bounded domain setting, global bifurcation diagram of multi-pulse solutions are shown by using new technique of double saddle-node bifurcation.

Mathematics Subject Classification

35J50 35J61 58J55 81V80 

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of MathematicsBeijing University of Chemical TechnologyBeijingPeople’s Republic of China
  2. 2.Department of MathematicsYunnan Normal UniversityKunmingPeople’s Republic of China
  3. 3.Department of MathematicsCollege of William and MaryWilliamsburgUSA

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