The exact solutions for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si11.svg"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mn>3</mml:mn> <mml:mo linebreak="badbreak">+</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> -dimensional Boiti-Leon-Manna-Pempinelli equation
Xiaofang Duan, J. G. Lü
Abstract
In the paper, we study the Boiti-Leon-Manna-Pempinelli equation with (3 + 1) dimension. By using the modified hyperbolic tangent function method, we obtain more new exact solutions for the (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation, which expand the solutions in previous literature. Those solutions have three forms determined according to the choice of parameters: trigonometric function form, rational function form, hyperbolic function form. Both trigonometric function form solutions and hyperbolic function form solutions include logarithmic function. And we give some examples and draw the some figures of the exact solutions.
Topics & Concepts
Hyperbolic functionFunction (biology)Trigonometric functionsDimension (graph theory)LogarithmRational functionMathematicsTrigonometrySigmoid functionPure mathematicsMathematical analysisApplied mathematicsGeometryComputer scienceArtificial neural networkArtificial intelligenceEvolutionary biologyBiologyNonlinear Waves and SolitonsFractional Differential Equations SolutionsAdvanced Differential Equations and Dynamical Systems