Local controllability and stability of the periodic fifth-order KdV equation with a nonlinear dispersive term

2021 ◽  
Vol 494 (1) ◽  
pp. 124635
Author(s):  
Jiawen Gu ◽  
Deqin Zhou
Keyword(s):  
Kdv Equation ◽  
Local Controllability ◽  
Fifth Order ◽  
Dispersive Term

Multi-symplectic method for generalized fifth-order KdV equation

2008 ◽  
Vol 17 (11) ◽  
pp. 3923-3929 ◽  
Author(s):  
Hu Wei-Peng ◽  
Deng Zi-Chen
Keyword(s):  
Kdv Equation ◽  
Symplectic Method ◽  
Fifth Order

Global Well-Posedness for the Fifth-Order KdV Equation in $$H^{-1}(\pmb {\mathbb {R}})$$

Annals of PDE ◽  
2021 ◽  
Vol 7 (2) ◽  
Author(s):  
Bjoern Bringmann ◽  
Rowan Killip ◽  
Monica Visan
Keyword(s):  
Kdv Equation ◽  
Well Posedness ◽  
Fifth Order

Construction of soliton solutions for modified Kawahara equation arising in shallow water waves using novel techniques

2020 ◽  
Vol 34 (07) ◽  
pp. 2050045 ◽  
Author(s):  
Naila Nasreen ◽  
Aly R. Seadawy ◽  
Dianchen Lu
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Nonlinear Problems ◽  
Applied Physics ◽  
Kawahara Equation ◽  
Generalized Riccati Equation ◽  
All Solutions ◽  
Fifth Order

The modified Kawahara equation also called Korteweg-de Vries (KdV) equation of fifth-order arises in shallow water wave and capillary gravity water waves. This study is based on the generalized Riccati equation mapping and modified the F-expansion methods. Several types of solitons such as Bright soliton, Dark-lump soliton, combined bright dark solitary waves, have been derived for the modified Kawahara equation. The obtained solutions have significant applications in applied physics and engineering. Moreover, stability of the problem is presented after being examined through linear stability analysis that justify that all solutions are stable. We also present some solution graphically in 3D and 2D that gives easy understanding about physical explanation of the modified Kawahara equation. The calculated work and achieved outcomes depict the power of the present methods. Furthermore, we can solve various other nonlinear problems with the help of simple and effective techniques.

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