scholarly journals Invariant Subspace and Classification of Soliton Solutions of the Coupled Nonlinear Fokas-Liu System

2019 ◽  
Vol 7 ◽  
Author(s):  
Aliyu Isa Aliyu ◽  
Yongjin Li ◽  
Dumitru Baleanu
Keyword(s):  
Invariant Subspace ◽  
Soliton Solutions ◽  
Liu System

Symmetry analysis, invariant subspace and conservation laws of the equation for fluid flow in porous media

2020 ◽  
Vol 17 (12) ◽  
pp. 2050173 ◽  
Author(s):  
Abdullahi Yusuf
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Conservation Laws ◽  
Invariant Subspace ◽  
Soliton Solutions ◽  
Flow In Porous Media ◽  
One Dimensional ◽  
Infinitesimal Generators ◽  
Lie Symmetry Method ◽  
Symmetry Method

The equation for fluid flow in porous media is analyzed in this paper with the aid of Lie symmetry method (LSM) and invariant subspace method (ISM). Infinitesimal generators, the entire geometric fields of the vectors and the symmetry groups of the equation being considered are given. One-dimensional optimal systems of sub-algebra are reported with corresponding reduced nonlinear ordinary differential equations. By means of ISM, we determine the exact solutions and invariant subspaces (ISs) for the equation under consideration. Moreover, with the aid of the new theorem of conservation, we establish the conservation laws (CLs) for the governing equation. The construction of the conserved vectors reveals the integrability and existence of soliton solutions of the equation for fluid flow in porous media.

scholarly journals Classification of the line-soliton solutions of KPII

2008 ◽  
Vol 41 (27) ◽  
pp. 275209 ◽  
Author(s):  
Sarbarish Chakravarty ◽  
Yuji Kodama
Keyword(s):  
Soliton Solutions ◽  
Line Soliton

scholarly journals Collision of water wave solitons

Open Physics ◽  
2013 ◽  
Vol 11 (11) ◽  
Author(s):  
Nora Fenyvesi ◽  
Gyula Bene
Keyword(s):  
Time Evolution ◽  
Water Wave ◽  
Boussinesq Equation ◽  
Soliton Solutions

AbstractA classification of the time evolution of the two-soliton solutions of the Boussinesq equation is given, based on the number of extrema of the wave. For solitons moving in the same directions, three different scenarios are found, while it is shown that only one of these scenarios exists in case of oppositely moving solitons.

On the classification of conservation laws and soliton solutions of the long short-wave interaction system

2018 ◽  
Vol 32 (18) ◽  
pp. 1850202 ◽  
Author(s):  
Mustafa Inc ◽  
Aliyu Isa Aliyu ◽  
Abdullahi Yusuf ◽  
Dumitru Baleanu
Keyword(s):  
Conservation Laws ◽  
Nonlinear Partial Differential Equations ◽  
Soliton Solutions ◽  
Wave Interaction ◽  
Expansion Method ◽  
Short Wave ◽  
Short Transverse ◽  
Interaction System ◽  
Conservation Theorem

In this paper, the classification of conservation laws (Cls) of the long short-wave interaction system (LSWS) which appears in fluid mechanics as well as plasma physics is implemented using two Cls theorems, namely, the multipliers approach and the new conservation theorem. The LSWS describes the interaction between one long longitudinal wave and one short transverse wave propagating in a generalized elastic medium. The zeroth-order multipliers and the nonlinear self-adjoint substitutions of the model are derived. Considering the fact that the new conservation theorem needs Lie point symmetries in constructing Cls, we derive the point symmetries of a system of nonlinear partial differential equations (NPDEs) acquired by transforming the model into real and imaginary components. Moreover, we derive some kink-type, bell-shaped, singular and combined soliton solutions to the model using the powerful sine-Gordon expansion method (SGEM). Some figures are presented to show the physical interpretations of the acquired results.

Note on the spectral classification of carbon stars in the photographic infrared region

1966 ◽  
Vol 24 ◽  
pp. 21-23
Author(s):  
Y. Fujita
Keyword(s):  
Infrared Region ◽  
Spectral Classification ◽  
Carbon Stars

We have investigated the spectrograms (dispersion: 8Å/mm) in the photographic infrared region fromλ7500 toλ9000 of some carbon stars obtained by the coudé spectrograph of the 74-inch reflector attached to the Okayama Astrophysical Observatory. The names of the stars investigated are listed in Table 1.

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