scholarly journals Airy kernel and Painlevé II

2002 ◽  
pp. 85-96 ◽  
Author(s):  
Craig Tracy ◽  
Harold Widom
Keyword(s):  
Airy Kernel ◽  
Painlevé Ii

On Ermakov–Painlevé II systems. Integrable reduction

Meccanica ◽  
2016 ◽  
Vol 51 (12) ◽  
pp. 2967-2974 ◽  
Author(s):  
Colin Rogers ◽  
Wolfgang K. Schief
Keyword(s):  
Painlevé Ii

scholarly journals Bilinear discrete Painleve-II and its particular solutions

1995 ◽  
Vol 28 (12) ◽  
pp. 3541-3548 ◽  
Author(s):  
J Satsuma ◽  
K Kajiwara ◽  
B Grammaticos ◽  
J Hietarinta ◽  
A Ramani
Keyword(s):  
Particular Solutions ◽  
Painlevé Ii

scholarly journals Matrix Painlevé II equations

2021 ◽  
Vol 207 (2) ◽  
pp. 560-571
Author(s):  
V. E. Adler ◽  
V. V. Sokolov
Keyword(s):  
Painlevé Ii

scholarly journals Asymptotics for the Sasa–Satsuma equation in terms of a modified Painlevé II transcendent

2020 ◽  
Vol 268 (12) ◽  
pp. 7480-7504 ◽  
Author(s):  
Lin Huang ◽  
Jonatan Lenells
Keyword(s):  
Painlevé Ii

Nonlocal Symmetry and its Applications in Perturbed mKdV Equation

2016 ◽  
Vol 71 (6) ◽  
pp. 557-564 ◽  
Author(s):  
Bo Ren ◽  
Ji Lin
Keyword(s):  
Constant Coefficient ◽  
Direct Method ◽  
Symmetry Transformation ◽  
Mkdv Equation ◽  
Nonlocal Symmetry ◽  
Rational Solutions ◽  
Initial Value ◽  
Interaction Solutions ◽  
Different Types ◽  
Painlevé Ii

AbstractBased on the modified direct method, the variable-coefficient perturbed mKdV equation is changed to the constant-coefficient perturbed mKdV equation. The truncated Painlevé method is applied to obtain the nonlocal symmetry of the constant-coefficient perturbed mKdV equation. By introducing one new dependent variable, the nonlocal symmetry can be localized to the Lie point symmetry. Thanks to the localization procedure, the finite symmetry transformation is presented by solving the initial value problem of the prolonged systems. Furthermore, many explicit interaction solutions among different types of solutions such as solitary waves, rational solutions, and Painlevé II solutions are obtained using the symmetry reduction method to the enlarged systems. Two special concrete soliton-cnoidal interaction solutions are studied in both analytical and graphical ways.

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