A special form of solution to complex valued Benjamin-Ono equations

被引：3

作者：

Huh, Hyungjin ^{[1
]}

机构：

[1] Chung Ang Univ, Dept Math, Seoul 06974, South Korea

来源：

PHYSICA D-NONLINEAR PHENOMENA | 2024年 / 463卷

基金：

新加坡国家研究基金会;

关键词：

Complex valued Benjamin-Ono equation; Finite time blowup; Cole-Hopf transformation; GLOBAL WELL-POSEDNESS; BLOW-UP; SOLITONS;

D O I：

10.1016/j.physd.2024.134171

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate a special form of solution to the complex valued Benjamin-Ono (cBO) equation. Under the special form of solution involving Hilbert transform, the complex valued (modified) Benjamin-Ono equations are equivalent to the quadratic (cubic) derivative Schr & ouml;dinger equations. The soliton interaction dynamics is used to construct a finite time blowup solution of the cBO equation on R. We also find static solutions. Applying Cole-Hopf transformation to quadratic derivative Schr & ouml;dinger equation, we derive a linear Schr & ouml;dinger equation with a special form of initial data from which some solutions to cBO equation can be obtained by an inverse transform.

引用

页数：5

共 18 条

[1] RATIONAL AND ELLIPTIC SOLUTIONS OF KORTEWEG DE-VRIES EQUATION AND A RELATED MANY-BODY PROBLEM [J].

AIRAULT, H ;

MCKEAN, HP ;

MOSER, J .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1977, 30 (01) :95-148

[2] UNIQUENESS AND RELATED ANALYTIC PROPERTIES FOR THE BENJAMIN-ONO-EQUATION - A NONLINEAR NEUMANN PROBLEM IN THE PLANE [J].

AMICK, CJ ;

TOLAND, JF .

ACTA MATHEMATICA, 1991, 167 (1-2) :107-126

[3] AN EXAMPLE OF BLOW-UP, FOR THE COMPLEX KDV EQUATION AND EXISTENCE BEYOND THE BLOW-UP [J].

BIRNIR, B .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1987, 47 (04) :710-725

[4] Blowup and ill-posedness for the complex, periodic KdV equation [J].

Bona, J. L. ;

Weissler, F. B. .

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2023, 25 (06)

[5] Pole dynamics of interacting solitons and blowup of complex-valued solutions of KdV [J].

Bona, Jerry L. ;

Weissler, Fred B. .

NONLINEARITY, 2009, 22 (02) :311-349

[6] ALGEBRAIC INTERNAL WAVE SOLITONS AND THE INTEGRABLE CALOGERO-MOSER-SUTHERLAND N-BODY PROBLEM [J].

CHEN, HH ;

LEE, YC ;

PEREIRA, NR .

PHYSICS OF FLUIDS, 1979, 22 (01) :187-188

[7] Normal form approach to global well-posedness of the quadratic derivative nonlinear Schrodinger equation on the circle [J].

Chung, Jaywan ;

Guo, Zihua ;

Kwon, Soonsik ;

Oh, Tadahiro .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2017, 34 (05) :1273-1297

[8]

Guo ZH, 2011, ADV DIFFERENTIAL EQU, V16, P1087

[9]

Ionescu AD, 2007, CONTEMP MATH, V428, P61

[10] Global well-posedness of the Benjamin-Ono equation in low-regularity spaces [J].

Ionescu, Alexandru D. ;

Kenig, Carlos E. .

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 20 (03) :753-798

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