An Exact Transformation from the Harry Dym Equation to the Modified KdV Equation

1985 ◽  
Vol 54 (5) ◽  
pp. 2055-2056 ◽  
Author(s):  
Shunji Kawamoto
Keyword(s):  
Kdv Equation ◽  
Modified Kdv Equation ◽  
Dym Equation ◽  
Harry Dym Equation

scholarly journals Self-Adjointness and Conservation Laws of Frobenius Type Equations

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1987
Author(s):  
Haifeng Wang ◽  
Yufeng Zhang
Keyword(s):  
Conservation Laws ◽  
Burgers Equation ◽  
Kdv Equation ◽  
The Self ◽  
Kp Equation ◽  
Commutative Subalgebra ◽  
Kompaneets Equation ◽  
Dym Equation ◽  
Harry Dym Equation

The Frobenius KDV equation and the Frobenius KP equation are introduced, and the Frobenius Kompaneets equation, Frobenius Burgers equation and Frobenius Harry Dym equation are constructed by taking values in a commutative subalgebra Z2ε in the paper. The five equations are selected as examples to help us study the self-adjointness of Frobenius type equations, and we show that the first two equations are quasi self-adjoint and the last three equations are nonlinear self-adjointness. It follows that we give the symmetries of the Frobenius KDV and the Frobenius KP equation in order to construct the corresponding conservation laws.

scholarly journals Explicit solutions to the semi-discrete modified KdV equation and motion of discrete plane curves

2012 ◽  
Vol 45 (4) ◽  
pp. 045206 ◽  
Author(s):  
Jun-ichi Inoguchi ◽  
Kenji Kajiwara ◽  
Nozomu Matsuura ◽  
Yasuhiro Ohta
Keyword(s):  
Kdv Equation ◽  
Plane Curves ◽  
Explicit Solutions ◽  
Modified Kdv Equation
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