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Cauchy Problem for Stochastic Nonlinear Schrödinger Equation with Nonlinear Energy-Critical Damping

Author

Listed:
  • Lijun Miao

    (School of Mathematics, Liaoning Normal University, Dalian 116029, China)

  • Linlin Qiu

    (School of Mathematics, Liaoning Normal University, Dalian 116029, China)

Abstract

We consider the Cauchy problem for the stochastic nonlinear Schrödinger equation augmented by nonlinear energy-critical damping term arising in nonlinear optics and quantum field theory. Through examining the behavior of the momentum and energy functionals, we almost surely prove the existence and uniqueness of global solutions with continuous H 1 ( R d ) valued paths. The results cover either defocusing nonlinearity in the full energy critical and subcritical range of exponents or focusing nonlinearity in the full subcritical range, as in the deterministic case.

Suggested Citation

  • Lijun Miao & Linlin Qiu, 2024. "Cauchy Problem for Stochastic Nonlinear Schrödinger Equation with Nonlinear Energy-Critical Damping," Mathematics, MDPI, vol. 12(16), pages 1-12, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:16:p:2501-:d:1455537
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    References listed on IDEAS

    as
    1. Biswas, Anjan, 2001. "Optical soliton perturbation with nonlinear damping and saturable amplifiers," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 56(6), pages 521-537.
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