A New $$(3+1)$$-dimensional Hirota Bilinear Equation: Its Bäcklund Transformation and Rational-type Solutions
K. Hosseini, Majid Samavat, Mohammad Mirzazadeh, Wen‐Xiu Ma, Zakia Hammouch
Abstract
The behavior of specific dispersive waves in a new $$(3+1)$$ -dimensional Hirota bilinear (3D-HB) equation is studied. A Bäcklund transformation and a Hirota bilinear form of the model are first extracted from the truncated Painlevé expansion. Through a series of mathematical analyses, it is then revealed that the new 3D-HB equation possesses a series of rational-type solutions. The interaction of lump-type and 1-soliton solutions is studied and some interesting and useful results are presented.
Topics & Concepts
Bilinear interpolationMathematicsBilinear transformTransformation (genetics)Type (biology)Series (stratigraphy)SolitonBilinear formMathematical analysisApplied mathematicsMathematical physicsPure mathematicsNonlinear systemPhysicsChemistryComputer scienceGeneFilter (signal processing)Computer visionEcologyBiochemistryQuantum mechanicsDigital filterBiologyStatisticsPaleontologyNonlinear Waves and SolitonsNonlinear Photonic SystemsAlgebraic structures and combinatorial models