Yutao Liu

doi:10.70711/eer.v2i7.5862

Existence of Solutions of Nonlinear Waveguide Schrodinger 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 Schringer 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.

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References

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

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

[2] J. Wei and Y. Wu, Normalized solutions for Schrodinger 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 Schrodinger equations, J. Math. Anal. Appl. 182 (1994), 409421.

[4] F.T Hioe, N coupled nonlinear Schrodinger 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 Schrodinger equations, Advances in

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

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

(1983), 486490.

[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

Schrodinger Equations. J Dyn DiffEquat, 33 (2021), 12971339.

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

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