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The features of ferromagnetic fluids make it supportive for an extensive range of usages in directing magnetic drugs and magnetic hyperthermia. Owing to all such potential applications, the current study is concerned with the ferromagnetic liquid flow past a stretching sheet with thermophoretic particle deposition and a magnetic dipole. The equations of described flow are transformed into ordinary differential equations (ODEs) by selecting suitable similarity variables. These ODEs are later solved numerically by the fourth and fifth-order Runge–Kutta–Fehlberg (RKF-45) technique by using a shooting scheme. The influence of sundry parameters on velocity, thermophoretic diffusive deposition velocity, skin-friction, Nusselt number, Sherwood number, thermal and concentration profiles are illustrated graphically. The results reveal that the increase in ferromagnetic interaction parameter improves the thermal profile but declines the velocity and concentration profiles. The imposition of thermophoretic particle deposition results in declination of the mass transfer. The escalating values of the ferromagnetic interaction parameter decline the rate of heat transfer. Finally, the rise in values of the thermophoretic parameter and thermophoretic coefficient decays thermophoretic diffusive deposition velocity. [ABSTRACT FROM AUTHOR]

ABSTRACT This manuscript focuses on the new wave behaviors of the system of equations for the ion sound wave under the action of the ponderomotive force which results from a nonlinear force that a charged particle experiences in an inhomogeneous oscillating electromagnetic field due to high-frequency field. The sine-Gordon expansion method which is one of the powerful methods has been considered for finding traveling wave solutions of the system of equations for the ion sound wave under the pressure of the Langmuir wave. This algorithm yields new complex hyperbolic function solutions to the system considered in this paper. Wolfram Mathematica 9 has been successfully used throughout the paper for mathematical calculations. [ABSTRACT FROM PUBLISHER]

In this study, a new method called improved Bernoulli sub-equation function method has been proposed. This method is based on the Bernoulli sub-ODE method. After we mention the general properties of proposed method, we apply this algorithm to the (2 + 1)-dimensional Boiti–Leon–Pempinelli equation system. This gives us some new prototype solutions such as exponential and rational function solutions. Then, we have plotted two- and three-dimensional surfaces of analytical solutions. Finally, we have submitted a comprehensive conclusion. [ABSTRACT FROM AUTHOR]

In this study, we obtain some new complex analytical solutions to the Kundu–Eckhaus equation which seems in the quantum field theory, weakly nonlinear dispersive water waves and nonlinear optics using improved Bernoulli sub-equation function method. After we have mentioned the general structure of improved Bernoulli sub-equation function method, we have successfully applied this method and then obtained some new complex hyperbolic and complex trigonometric function solutions. Two- and three-dimensional surfaces of analytical solutions have been plotted via wolfram Mathematica 9 version. At the end of this article, a conclusion has been submitted by mentioning important points founded in this study. [ABSTRACT FROM AUTHOR]

In this study, we have studied to obtain some new analytical solutions to the (1 + 1)-dimensional nonlinear Dispersive Modified Benjamin–Bona–Mahony equation by using modified exp-function method. We have submitted the general structure of modified exp-function method. We have founded some new analytical solutions such as hyperbolic and rational function solutions. Afterward, we have plotted 2D and 3D surfaces of analytical solutions obtained in this study by using computer programming wolfram Mathematica 9. [ABSTRACT FROM AUTHOR]