Nonlinear excitations in negative index materials: Modulational instability and solitary wave solutions

2016 ◽  
Author(s):  
Vivek Kumar Sharma ◽  
Amit Goyal
Keyword(s):  
Solitary Wave ◽  
Modulational Instability ◽  
Negative Index ◽  
Solitary Wave Solutions ◽  
Negative Index Materials ◽  
Nonlinear Excitations ◽  
Wave Solutions

Periodic and solitary wave solutions for ultrashort pulses in negative-index materials

2013 ◽  
Vol 60 (10) ◽  
pp. 836-840 ◽  
Author(s):  
Vivek Kumar Sharma ◽  
Amit Goyal ◽  
Thokala Soloman Raju ◽  
C.N. Kumar
Keyword(s):  
Solitary Wave ◽  
Ultrashort Pulses ◽  
Negative Index ◽  
Solitary Wave Solutions ◽  
Negative Index Materials ◽  
Wave Solutions

scholarly journals Construction of new solitary wave solutions of generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony and simplified modified form of Camassa-Holm equations

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 896-909 ◽  
Author(s):  
Dianchen Lu ◽  
Aly R. Seadawy ◽  
Mujahid Iqbal
Keyword(s):  
Solitary Wave ◽  
Nonlinear Partial Differential Equations ◽  
Research Work ◽  
Traveling Wave Solutions ◽  
Elliptic Functions ◽  
Mapping Method ◽  
New Method ◽  
Auxiliary Equation ◽  
Solitary Wave Solutions ◽  
Wave Solutions

AbstractIn this research work, for the first time we introduced and described the new method, which is modified extended auxiliary equation mapping method. We investigated the new exact traveling and families of solitary wave solutions of two well-known nonlinear evaluation equations, which are generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony and simplified modified forms of Camassa-Holm equations. We used a new technique and we successfully obtained the new families of solitary wave solutions. As a result, these new solutions are obtained in the form of elliptic functions, trigonometric functions, kink and antikink solitons, bright and dark solitons, periodic solitary wave and traveling wave solutions. These new solutions show the power and fruitfulness of this new method. We can solve other nonlinear partial differential equations with the use of this method.

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