Characteristics of solitary waves on a running film down an inclined plane under an electrostatic field

Propagation of three-dimensional nonlinear solitary waves in a magnetized electron–positron plasma is analyzed. Modified extended mapping method is further modified and applied to three-dimensional nonlinear modified Zakharov–Kuznetsov equation to find traveling solitary wave solutions. As a result, electrostatic field potential, electric field, magnetic field and quantum statistical pressure are obtained with the aid of Mathematica. The new exact solitary wave solutions are obtained in different forms such as periodic, kink and anti-kink, dark soliton, bright soliton, bright and dark solitary waves, etc. The results are expressed in the forms of trigonometric, hyperbolic, rational and exponential functions. The electrostatic field potential and electric and magnetic fields are shown graphically. The soliton stability of these solitary wave solutions is analyzed. These results demonstrate the efficiency and precision of the method that can be applied to many other mathematical physical problems.

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Evolution mechanism of solitary waves on the inviscid film flow under an electrostatic field

Journal of Mechanical Science and Technology ◽

10.1007/s12206-018-0523-z ◽

2018 ◽

Vol 32 (6) ◽

pp. 2659-2669

Author(s):

Sunyoung Park ◽

Gun Woo Kim ◽

Gwang Hoon Rhee ◽

Hyo Kim

Keyword(s):

Solitary Waves ◽

Electrostatic Field ◽

Film Flow ◽

Evolution Mechanism

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Oblique runup of non-breaking solitary waves on an inclined plane

Journal of Fluid Mechanics ◽

10.1017/s0022112010005343 ◽

2011 ◽

Vol 668 ◽

pp. 582-606 ◽

Cited By ~ 6

Author(s):

GEIR K. PEDERSEN

Keyword(s):

Solitary Wave ◽

Solitary Waves ◽

Evolution Equations ◽

Boussinesq Equations ◽

Normal Incidence ◽

Finite Depth ◽

Breaking Waves ◽

Wave Pattern ◽

Angle Of Incidence ◽

Inclined Plane

When a wave of permanent form is obliquely incident on an inclined plane, the wave pattern becomes stationary in a frame of reference which moves along the shore. This enables a simplified mathematical description of the problem which is used herein as a basis for efficient and accurate numerical simulations. First, a nonlinear and weakly dispersive set of Boussinesq equations for the downstream evolution of such stationary patterns is derived. In the hydrostatic approximation, streamline-based Lagrangian versions of the evolution equations are developed for automatic tracing of the shoreline. Both equation sets are, in their present form, developed for non-breaking waves only. Finite difference models for both equation sets are designed. These methods are then coupled dynamically to obtain a single nonlinear model with dispersive wave propagation in finite depth and an accurate runup representation. The models are tested by runup of waves at normal incidence and comparison with a more general model for the refraction of a solitary wave on a slope. Finally, a set of runup computations for oblique solitary waves is performed and compared with estimates of oblique runup heights obtained from a combination of an analytic solution for normal incidence and optics. We find that the runup heights decrease in proportion to the square of the angle of incidence for angles up to 45°, for which the height is reduced by around 12% relative to that of normal incidence. In Appendix A, the validity of the downstream formulation is discussed in the light of solitary wave optics and wave jumps.

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