Standing waves for a relativistic quasilinear asymptotically Schrödinger equation

Abstract

In this paper, we study the standing waves for the relativistic quasilinear asymptotically Schrödinger equation

This model has been proposed in the self-channelling of a high-power ultrashort laser in matter.

Keywords:

• Quasilinear Schrödinger equation
• Mountain Pass Theorem
• soliton solutions

AMS Subject Classifications:

• 35B33
• 35J20
• 35J60
• 35Q55

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by NSFC [Nos. 11201154], [11371146]; the Fundamental Research Funds for the Central Universities [No. 2014ZZ0065]; Research fund for the Doctoral Program of Higher Education [No. 20120172120040].