scholarly journals Travelling wave solution of the weakly nonlinear evolution equation with control term

2011 ◽  
Vol 60 (5) ◽  
pp. 050204
Author(s):  
Mo Jia-Qi ◽  
Cheng Rong-Jun ◽  
Ge Hong-Xia
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Wave Solution ◽  
Nonlinear Evolution ◽  
Travelling Wave ◽  
Travelling Wave Solution ◽  
Weakly Nonlinear

A mechanism for rivulet formation in heated falling films

1996 ◽  
Vol 321 ◽  
pp. 279-298 ◽  
Author(s):  
S. W. Joo ◽  
S. H. Davis ◽  
S. G. Bankoff
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Heated Plate ◽  
Weakly Nonlinear ◽  
Transfer Rates ◽  
Weakly Nonlinear Analysis ◽  
Flow And Heat Transfer ◽  
Long Wave ◽  
Rivulet Formation

We consider a long-wave evolution equation that governs a draining film on a heated plate and hence is capable of describing both surface-wave and thermocapillary instabilities. When the flow and heat transfer rates are moderate, we show, via weakly nonlinear analysis of a truncated system and numerical simulation of the full nonlinear evolution equation, that coupled temporal instabilities can create surface deformations that lead to an array of rivulets aligned with the flow. This work thus demonstrates a mechanism of rivulet formation based solely on instability phenomena.

Dark and new travelling wave solutions to the nonlinear evolution equation

Optik ◽  
2016 ◽  
Vol 127 (19) ◽  
pp. 8043-8055 ◽  
Author(s):  
Haci Mehmet Baskonus ◽  
Dilara Altan Koç ◽  
Hasan Bulut
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions

New (3+1)-dimensional nonlinear evolution equation: multiple soliton solutions

2014 ◽  
Vol 4 (4) ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Multiple Soliton Solutions ◽  
Simplified Hirota’S Method ◽  
Hirota's Method

AbstractIn this work, we introduce an extended (3+1)-dimensional nonlinear evolution equation. We determine multiple soliton solutions by using the simplified Hirota’s method. In addition, we establish a variety of travelling wave solutions by using hyperbolic and trigonometric ansatze.

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