scholarly journals GEOMETRICAL ASPECTS OF AN INTEGRABLE NONLINEAR EQUATION OF THE SCHWARZIAN TYPE

2003 ◽  
Author(s):  
A. TONGAS
Keyword(s):  
Nonlinear Equation ◽  
Integrable Nonlinear Equation

scholarly journals An integrable fourth-order nonlinear evolution equation applied to surface redistribution due to capillarity

1997 ◽  
Vol 38 (4) ◽  
pp. 518-541 ◽  
Author(s):  
Peter Tritscher
Keyword(s):  
Nonlinear Equation ◽  
Surface Diffusion ◽  
Anisotropic Material ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Constitutive Relations ◽  
Nonlinear Evolution Equations ◽  
Surface Evolution ◽  
Integrable Nonlinear Equation ◽  
Closed Form Solutions

AbstractMembers of an hierarchy of integrable nonlinear evolution equations, related to the well-known linearizable diffusion equation which has the diffusivity form as the reciprocal of the square of the concentration, are adapted to derive a new integrable nonlinear equation which models the surface evolution of an arbitrarily-oriented theoretical anisotropic material by the concomitant action of evaporation-condensation and surface diffusion. The constitutive relations are explicitly formulated and these show that the theoretical anisotropic material behaves like a liquid crystal. The integrable nonlinear equation may be used to advantage as test cases for numerical schemes. Its form has many attributes of the nonlinear governing equation for an isotropic material. Closed-form solutions are constructed for the evolution of a ramped surface by concomitant evaporation-condensation and surface diffusion.

scholarly journals A new fourth-order integrable nonlinear equation: breather, rogue waves, other lump interaction phenomena, and conservation laws

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Dumitru Baleanu ◽  
Ali Saleh Alshomrani ◽  
Malik Zaka Ullah
Keyword(s):  
Nonlinear Equation ◽  
Conservation Laws ◽  
Fourth Order ◽  
Rogue Waves ◽  
Adjoint Representation ◽  
Integrable Nonlinear Equation ◽  
3 Dimensional ◽  
Invariance Properties ◽  
Dynamical Characteristics ◽  
Hirota Bilinear

AbstractIn this study, we investigate a new fourth-order integrable nonlinear equation. Firstly, by means of the efficient Hirota bilinear approach, we establish novel types of solutions which include breather, rogue, and three-wave solutions. Secondly, with the aid of Lie symmetry method, we report the invariance properties of the studied equation such as the group of transformations, commutator and adjoint representation tables. A differential substitution is found by nonlinear self-adjointness (NSA) and thereafter the associated conservation laws are established. We show some dynamical characteristics of the obtained solutions through via the 3-dimensional and contour graphs.

Determination of Approximated Root of Nonlinear Equation by Interpolation Technique

2018 ◽  
Vol 50 (001) ◽  
pp. 133-136
Author(s):  
M. B. BROHI ◽  
A. A. SHAIKH ◽  
S. BHATTI ◽  
S. QUERSHI
Keyword(s):  
Nonlinear Equation ◽  
Interpolation Technique
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