Higher Order Nonlinear Schrödinger Equation in Domains With Moving Boundaries
Raúl Nina-Mollisaca
Unidad de posgrado, Universidad Nacional Jorge Basadre Grohmann, Tacna, Peru
Search for more papers by this authorCorresponding Author
Mauricio Sepúlveda-Cortés
DIM and CI2MA, Universidad de Concepción, Concepción, Chile
Correspondence:
Mauricio Sepúlveda-Cortés ([email protected])
Search for more papers by this authorRodrigo Véjar-Asem
Departamento de Matemáticas, Universidad de la Serena, La Serena, Chile
Search for more papers by this authorOctavio Vera-Villagrán
Departamento de Matemática, Universidad de Tarapacá, Arica, Chile
Search for more papers by this authorRaúl Nina-Mollisaca
Unidad de posgrado, Universidad Nacional Jorge Basadre Grohmann, Tacna, Peru
Search for more papers by this authorCorresponding Author
Mauricio Sepúlveda-Cortés
DIM and CI2MA, Universidad de Concepción, Concepción, Chile
Correspondence:
Mauricio Sepúlveda-Cortés ([email protected])
Search for more papers by this authorRodrigo Véjar-Asem
Departamento de Matemáticas, Universidad de la Serena, La Serena, Chile
Search for more papers by this authorOctavio Vera-Villagrán
Departamento de Matemática, Universidad de Tarapacá, Arica, Chile
Search for more papers by this authorFunding: The second author MSC was partially financed by Fondecyt-ANID 1220869 project, ECOS200018 ANID Project and Centro de Modelamiento Matemático (CMM), Universidad de Chile, FB210005, BASAL funds for centers of excellence from ANID-Chile. The fourth author OVV was partially financed by projects UTA MAYOR 2022–2023, 4764-22 and UTA MAYOR 2023–2024, 4772-23.
ABSTRACT
The initial boundary value problem in a bounded domain with moving boundaries and nonhomogeneous boundary conditions for a higher order nonlinear Schrödinger (HNLS) equation is considered. Existence and uniqueness of global weak solutions are proved as well as the stability of the solution. Additionally, a conservative numerical method of finite differences is introduced that also verifies stability properties with respect to the -norm, and along with proving its convergence, some interesting numerical examples are shown that illustrate the behavior of the solution.
Conflicts of Interest
The authors declare no conflicts of interest.
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