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On the asymptotic behavior of solutions for a nonlinear Schrödinger system

Author

Listed:
  • Vicente C. P. Alvarez

    (Nazarbayev University, Department of Mathematics)

  • Ademir Pastor

    (Universidade Estadual de Campinas (UNICAMP), Departamento do Matemática, Instituto de Matemática, Estatística Computação Científica (IMECC))

Abstract

We deal with the construction of some special solutions for a two-component nonlinear Schrödinger system. More precisely, let $$R_1$$ R 1 and $$R_2$$ R 2 be two traveling waves of a scalar Schrödinger equation; our goal is to construct a solution of the system which behave at infinity like the pair $$(R_1,R_2)$$ ( R 1 , R 2 ) . Initially, we prove the existence of such solutions in dimensions $$1\le d\le 3$$ 1 ≤ d ≤ 3 with the assumption of relative high speeds between the solitary waves. We then finish our results by studying the one-dimensional case without the assumption of relative high speeds. The main tools used to establish our results combine several techniques including energy estimates, bootstrap, modulation and localization arguments.

Suggested Citation

  • Vicente C. P. Alvarez & Ademir Pastor, 2026. "On the asymptotic behavior of solutions for a nonlinear Schrödinger system," Partial Differential Equations and Applications, Springer, vol. 7(3), pages 1-42, June.
    • Handle: RePEc:spr:pardea:v:7:y:2026:i:3:d:10.1007_s42985-025-00329-y
    DOI: 10.1007/s42985-025-00329-y
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