Abstract
In this paper, to find new wave structures of (2 + 1)-dimensional new generalized Korteweg-de Vries (ngKdV) equation, extended generalized Kudryashov and improved tan(ϕ2)-expansion approaches are utilized. Both approaches are based on the use of a traveling wave transformation and an auxiliary equation. As a result, a variety of solutions including exponential, hyperbolic and rational functions are retrieved. To explain the dynamics of soliton profiles, a graphical depiction of newly discovered solutions for appropriate parametric values is also presented. It has been acknowledged that the approaches utilized are effective and influential instruments for developing solitary wave solutions to nonlinear problems found in mathematical physics.
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