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This work addresses the four main inducements: Lump, rogue wave, Homoclinic breather and multi-wave solutions for (2+1)-Modified Veronese Web (MVW) equation via Hirota bilinear approach and the ansatz technique. This model is a linearly degenerate integrable nonlinear partial differential equation (NLPDE) and can also be used to admit a differential covering with nonremoval physical parameters. By assuming the function f in the Hirota bilinear form of the presented model as the general quadratic function, trigonometric function and exponential function form, also with appropriate set of parameters, we have prevented the lump, rogue wave, breather and multi-wave solutions successfully. A precise compatible wave transformation is utilized to obtain multi-wave solutions of governing model. Also, the motion track of the lump, Rogue wave and multi-waves is also explained both physically and theoretically. These new results contain some special arbitrary constants that can be useful to spell out diversity in qualitative features of wave phenomena. [ABSTRACT FROM AUTHOR]

We successfully apply extended rational sine-cosine/sinh-cosh and advance expansion function techniques in this paper. Various kinds of soliton solutions to the conformable time-fractional resonant nonlinear Schrödinger equation (RNLSE) in optical fiber are extracted. We discuss the system with the effects of coefficients like group velocity dispersion, non-Kerr nonlinearity, resonant nonlinearity, and construct optical soliton solution in terms of rational, trigonometric and hyperbolic function solutions with arbitrary parameters. The recovered solutions reveal that the applied approaches are straightforward and efficient to work out the excellent contribution for analyzing several classes of nonlinear partial differential equations (NLPDEs) in engineering and sciences. Moreover, 3D, 2D and contour graphs are sketched with suitable selection of the parameters under the criteria of constraints conditions. [ABSTRACT FROM AUTHOR]