2011
DOI: 10.1088/0253-6102/56/2/04
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Binary Bell Polynomials Approach to Generalized Nizhnik—Novikov—Veselov Equation

Abstract: The elementary and systematic binary Bell polynomials method is applied to the generalized Nizhnik-Novikov-Veselov (GNNV) equation. The bilinear representation, bilinear Bäcklund transformation, Lax pair and infinite conservation laws of the GNNV equation are obtained directly, without too much trick like Hirota's bilinear method.

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Cited by 18 publications
(10 citation statements)
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“…where W tends to a constant and its derivatives vanish as |X| → ∞. The dependent variable transformation (28) means that…”
Section: A the Transformation Process Of The Mgvementioning
confidence: 99%
See 2 more Smart Citations
“…where W tends to a constant and its derivatives vanish as |X| → ∞. The dependent variable transformation (28) means that…”
Section: A the Transformation Process Of The Mgvementioning
confidence: 99%
“…Recently, the Bell polynomials are found to play an important role in the characterization of integrability of NLEEs. [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] As is well known, the Hirota direct method 32, 33 is a powerful tool for investigating integrability of the NLEEs. Once bilinear equation of the NLEE is given, one can construct its corresponding multi-soliton solutions, quasiperiodic solutions, Wronskian solutions, bilinear Bäcklund transformation, etc.…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…[4] The elementary and systematic binary Bell polynomials method has been applied to this equation. [5] The bilinear representation, bilinear Bäcklund transformation (BT), Lax pair and infi-nite conservation laws of this equation have been obtained directly, without too much trick like Hirota's bilinear method. Applying the truncated Painlevé expansion to the (2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov (ANNV) system, some BTs including auto and non-auto ones have been obtained.…”
Section: Introductionmentioning
confidence: 99%
“…[20] Lou presented two sets of generalized symmetries of the potential NNV equation by a formal series symmetry method [21] and studied the coherent structures of the NNV equation in [22]. With the binary Bell polynomials method, Hu and Chen [23] derived the bilinear representation, bilinear Bäcklund transformation, Lax pair and infinite conservation laws for the NNV equation. Wazwaz [24] derived the multiple soliton solutions with the help of a simplified form of the Hirotas bilinear method.…”
Section: Introductionmentioning
confidence: 99%