New exact solutions for the (2 + 1)-dimensional generalized Broer–Kaup system

• Published in: Applied mathematics and computation Vol. 199; no. 2; pp. 572 - 580
• Main Authors: Lu, Dianchen, Hong, Baojian
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 01.06.2008; Elsevier
• Subjects: Exact sciences and technology; Generalized Broer–Kaup equations; Global analysis, analysis on manifolds; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Partial differential equations; Periodic-like solutions; Riccati equations; Sciences and techniques of general use; Soliton-like solutions; Special functions; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; Generalized Broer–Kaup equations; Periodic-like solutions; Riccati equations; Soliton-like solutions; Numerical analysis; Wave propagation; Applied mathematics; Riccati equation; Periodic solution; Shallow water; Arbitrary function; Generalized Broer-Kaup equations; Exact solution
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2007.10.012

The (1 + 1)-dimensional Broer–Kaup system, which describes the propagation of shallow water waves, is extended to a generalized (2 + 1)-dimensional model with Painleve property. In this paper, based on the general variable separation approach and two extended Riccati equations, we first find several new families of exact soliton-like solutions and periodic-like wave solutions with arbitrary functions for the (2 + 1)-dimensional simplified generalized Broer–Kaup (GBK) system ( B = 0). Abundant new localized excitations can be found by selecting appropriate functions. After that, we consider the conditions of ( B ≠ 0) to the GBK, and several new results are obtained.