Study on the (2+1)-dimensional extension of Hietarinta equation: soliton solutions and Bäcklund transformation
Di Gao, Xing Lü, Mingshu Peng
Abstract
Abstract The (1+1)-dimensional bilinear Hietarinta equation was firstly proposed when searching for integrable nonlinear evolution equations by the three-soliton method. In this paper, we focus on the (2+1)-dimensional extension of Hietarinta equation, which enjoys potential application in environmental engineering. Based on the bilinear form, one-soliotn and two-soliton solutions are derived. Bilinear Bäcklund transformation and Bell-polynomial-typed Bäcklund transformation are derived through the Hirota bilinear method and Bell polynomials, respectively. The three-dimensional plots of soliton solutions have been given by selecting appropriate parameters.
Topics & Concepts
Bilinear interpolationExtension (predicate logic)Transformation (genetics)Integrable systemBilinear transformMathematicsBell polynomialsSolitonPolynomialBilinear formApplied mathematicsOne-dimensional spaceFocus (optics)Nonlinear systemMathematical physicsPure mathematicsMathematical analysisPhysicsComputer scienceQuantum mechanicsStatisticsBiochemistryFilter (signal processing)GeneDigital filterComputer visionProgramming languageChemistryOpticsNonlinear Waves and SolitonsNonlinear Photonic SystemsAlgebraic structures and combinatorial models