Investigating travelling wave solutions of the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation through the two analytical techniques

Abstract The wave phenomenon of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mfenced close=")" open="("> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:mfenced> </mml:mrow> </mml:math> -dimensional Boiti-Leon-Manna-Pempinelli (BLMP) is an asset for investigating the dynamic behavior of waves in fluid dynamics, water wave mechanics, ocean engineering, and science. In this investigation, the object of the research is to explore abundant explicit traveling wave solutions for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mfenced close=")" open="("> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:mfenced> </mml:mrow> </mml:math> -dimensional BLMP equation. The new auxiliary equation (NAE) and unified techniques are applied to the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mfenced close=")" open="("> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:mfenced> </mml:mrow> </mml:math> -dimensional BLMP equation and obtained plenty of analytical solutions, including trigonometric, hyperbolic, exponential, and rational function solutions. The attained results are stated in a few graphs in three-dimensional (3D), contour, and two-dimensional (2D) figures, where 2D figures also describe the effect of wave properties to help better understand the dynamic behaviors. Based on time, the influence of the free parameter on wave type is comprehensively investigated using various figures, demonstrating the significant impact of nonlinearity. These graphical representations are based on specific parameter values, which aid in understanding the model’s complex general behavior. However, this study’s findings are compared to those acquired in published literature conducted by other experts. The results show that the technique is successful and reliable, making it appropriate for general usage in a variety of sophisticated nonlinear models. Finally, these techniques are effectively generating novel explicit traveling wave solutions from the nonlinear evolution equations that have vital significance in applied science and engineering.