pisco_log
banner

Existence of Solutions of Nonlinear Waveguide Schr¨odinger Equation

Yutao Liu

Abstract


In this paper, we study the of the existence of the solution of the Schrodinger equation with mixed nonlinear terms under a full wave
guide Schrödinger flow on a cylindrical domain R × T. Mainly applying variational methods, we prove that there exists a solution such that
the first derivative of the functional is equal to 0,which proves the existence of the nonlinear Schrodinger equation.

Keywords


Nonlinear Schrödinger equation; Minimizing Sequence; The Lagrange multiplier

Full Text:

PDF

Included Database


References


[1] Kawata, T., Sakai, J. Kobayashi, N. Inverse Method for the Mixed Nonlinear Schr¨odinger Equation and Soliton Solutions, Journal of

the Physical Society of Japan .48(1979), 1371-1379.

[2] J. Wei and Y. Wu, Normalized solutions for Schr¨odinger equations with critical Sobolev exponent and mixed nonlinearities, Journal of

Functional Analysis. 283 (2022), 109574.

[3] S. Tan, L. Zhang, On a weak solution of the mixed nonlinear Schr¨odinger equations, J. Math. Anal. Appl. 182 (1994), 409–421.

[4] F.T Hioe, N coupled nonlinear Schr¨odinger equations with mixed nonlinear interactions, Physics Letters A. 304 (2002), 30-35.

[5] D. Shi and H. Yang, Unconditionally optimal error estimates of a new mixed FEM for nonlinear Schr¨odinger equations, Advances in

Computational Mathematics. 45 (2019), 3173-3194.

[6] Br´ezis, H., Lieb, E. A relation between pointwise convergence of functions and convergence of functionals, Proc. Am. Math. Soc. 88

(1983), 486–490.

[7] L. Boccardo, T. Gallouet, Compactness of minimizing sequences, Nonlinear Analysis. 137 (2016), 213- 221.

[8] Bahri, Y., Ibrahim, S and Kikuchi, H. Transverse Stability of Line Soliton and Characterization of Ground State for Wave Guide

Schr¨odinger Equations. J Dyn DiffEquat, 33 (2021), 1297–1339.




DOI: http://dx.doi.org/10.70711/eer.v2i7.5862

Refbacks

  • There are currently no refbacks.