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This paper focuses on the instability modulation and new travelling wave solutions of the (2 + 1)-dimensional Kundu–Mukherjee–Naskar equation via the tanh function method. Dark, mixed dark–bright, complex solitons and periodic wave solutions are archived. Strain conditions for the validity of results are also reported. Instability modulation properties of the governing model are also extracted. Various wave simulations in 2D, 3D and contour graphs under the strain conditions are presented. [ABSTRACT FROM AUTHOR]

In this work, we investigate the perturbed optical solitons to the Gerdjikov-Ivanov equation consisting of group velocity dispersion and quintic nonlinearity coefficients, which communicate the propagation of pulses in nonlinear optics. The various kinds of solitons in single and combined forms like dark, singular, dark-singular, bright-dark are derived by Fan-extended sub equation method. Moreover, the singular periodic, triangular type solutions are also obtained. And, we also discuss the stability analysis of the studied nonlinear model with the concept of linear stability, we prove that the governing model is stable. Parametric conditions on physical parameters to ensure the existence criteria of optical solitons are also listed. We also plot 3D profiles for the physical behavior of the obtained solutions by selecting the suitable values of the parameters. [ABSTRACT FROM AUTHOR]

This work deals with finding new complex solitons to the perturbed nonlinear Schrödinger model with the help of an analytical method. Using several computation programs, we gain entirely new solitons to the considering model. Under the choice of suitable values of the parameters, density graphs to the reported solutions, such as complex, hyperbolic, trigonometric and exponential, are successfully presented. Simulations in various dimensions are also plotted by using package programs. [ABSTRACT FROM AUTHOR]