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The time-fractional generalized biological population model and the (2, 2, 2) Zakharov–Kuznetsov (ZK) equation are significant modeling equations to analyse biological population, ion-acoustic waves in plasma, electromagnetic waves, viscoelasticity waves, material science, probability and statistics, signal processing, etc. The new generalized G ′ / G -expansion method is consistent, computer algebra friendly, worthwhile through yielding closed-form general soliton solutions in terms of trigonometric, rational and hyperbolic functions associated to subjective parameters. For the definite values of the parameters, some well-established and advanced solutions are accessible from the general solution. The solutions have been analysed by means of diagrams to understand the intricate internal structures. It can be asserted that the method can be used to compute solitary wave solutions to other fractional nonlinear differential equations by means of fractional complex transformation. [ABSTRACT FROM AUTHOR]

Fractional nonlinear evolution equations concerning conformable fractional derivative are effective models to interpret intricate physical phenomena in the real world. The space-time fractional foam drainage equation and the coupled mKdV equations with conformable fractional derivative are important model equations for shallow water waves, the waves of flow of liquid between bubbles, the capillary waves, the waves of foam density, the electro-hydro-dynamical model, the ion acoustic plasma waves etc. In this study, we extract the functional and further general exact wave solutions comprising the rational, trigonometric, exponential and hyperbolic functions to the above stated models taking the advantage of the auxiliary equation method with the assistance of the fractional complex transformation. The method is convenient, reliable and delivers fresh and useful solutions to fractional differential equations ascend in physical and engineering sciences. We depict figures of the obtained solutions in order to illustrate the inner structure associated to the phenomena. [ABSTRACT FROM AUTHOR]

This paper concerns with the integrability of variable coefficient fifth order nonlinear Schrödinger's equation describing the dynamics of attosecond pulses in inhomogeneous fibers. Variable coefficients incorporate varying dispersion and nonlinearity which are of physical significance in considering the nonuniform boundaries of fibers as well as the inhomogeneities of the media. The well-known exp(−φ(s))-expansion method is used to retrieve singular and periodic solitons with the aid of symbolic computation. The structures of the obtained solutions are discussed along with their existence criteria. Moreover, the modulation instability analysis is carried out to identify the instability regions. A dispersion relation is extracted between wave number and frequency. The optimal value of the frequency is found for the occurrence of the instability. A detailed discussion of the results is also given along with graphics. [ABSTRACT FROM AUTHOR]