KP方程式

KP方程式 (テンプレート:Lang-en-short) は非線形波動・水面波を記述する偏微分方程式であり、次のように表わされる。

\partial_{x} (\partial_{t} u + u \partial_{x} u + ϵ^{2} \partial_{x x x} u) + λ \partial_{y y} u = 0, λ = \pm 1 .

KdV方程式の2次元版方程式であり、KdV方程式と並ぶ可積分系・ソリトン方程式の代表例である。

変種

Gardner-KP 方程式^[1]^[2]^[3]^[4]
KP-Boussinesq 方程式^[5]^[6]
Lax-KP 方程式^[7]
超離散KP方程式 (テンプレート:Lang-en-short)^[8]^[9]^[10]

KP方程式に関連した業績のある研究者

海外

日本

薩摩順吉^[15]^[16]^[17]^[18]^[19]^[19]^[20]
佐藤幹夫 (数学者)-佐藤理論
神保道夫 (三輪哲二、柏原正樹などとの共同研究)^[21]^[22]^[23]^[24]^[25]
広田良吾^[9]^[10]^[15]^[26]
和達三樹^[27]

出典

テンプレート:Reflist

参考文献

テンプレート:参照方法

テンプレート:Cite journal. Translation of テンプレート:Cite journal
テンプレート:SpringerEOM
Kodama, Y. (2017). KP Solitons and the Grassmannians: combinatorics and geometry of two-dimensional wave patterns. Springer.
時弘哲治、箱玉系の数理、朝倉書店。

外部リンク

テンプレート:Mathworld
テンプレート:Scholarpedia
テンプレート:URL (The KP page by Bernard Deconinck, University of Washington, Department of Applied Mathematics)

テンプレート:Mathanalysis-stub

↑ Wazwaz, A. M. (2008). Solitons and singular solitons for the Gardner–KP equation. Applied Mathematics and Computation, 204(1), 162-169.
↑ Xu, B., & Liu, X. Q. (2009). Classification, reduction, group invariant solutions and conservation laws of the Gardner-KP equation. Applied mathematics and computation, 215(3), 1244-1250.
↑ Naz, R., Ali, Z., & Naeem, I. (2013). Reductions and new exact solutions of ZK, Gardner KP, and modified KP equations via generalized double reduction theorem. In Abstract and Applied Analysis (Vol. 2013). Hindawi.
↑ Jawad, A. J. A. M., Mirzazadeh, M., & Biswas, A. (2015). Dynamics of shallow water waves with Gardner–Kadomtsev–Petviashvili equation. Discrete and Continuous Dynamical Systems, Series S, 8(6), 1155-1164.
↑ Wazwaz, A. M., & El-Tantawy, S. A. (2017). Solving the $(3 + 1)$ -dimensional KP–Boussinesq and BKP–Boussinesq equations by the simplified Hirota’s method. Nonlinear Dynamics, 88(4), 3017-3021.
↑ Sun, B., & Wazwaz, A. M. (2018). General high–order breathers and rogue waves in the $(3 + 1)$ -dimensional KP–Boussinesq equation. Communications in Nonlinear Science and Numerical Simulation, 64, 1-13.
↑ Wazwaz, A. M. (2008). Multiple-soliton solutions for the Lax–Kadomtsev–Petviashvili (Lax–KP) equation. Applied Mathematics and computation, 201(1-2), 168-174.
↑ Tokihiro, T., Takahashi, D., & Matsukidaira, J. (2000). Box and ball system as a realization of ultradiscrete nonautonomous KP equation. Journal of Physics A: Mathematical and General, 33(3), 607.
↑ ^9.0 ^9.1 Shinzawa, N., & Hirota, R. (2003). The Bäcklund transformation equations for the ultradiscrete KP equation. Journal of Physics A: Mathematical and General, 36(16), 4667.
↑ ^10.0 ^10.1 新沢信彦, & 広田良吾. (2003). 超離散 KP 方程式, 超離散 BKP 方程式の Backlund 変換方程式 (可積分系研究の新展開: 連続・離散・超離散).
↑ Krichever, I. M., & Novikov, S. P. (1978). Holomorphic bundles over Riemann surfaces and the Kadomtsev—Petviashvili equation. I. Functional Analysis and Its Applications, 12(4), 276-286.
↑ Fokas, A. S., & Ablowitz, M. J. (1983). Method of solution for a class of multidimensional nonlinear evolution equations. Physical Review Letters, 51(1), 7.
↑ Fokas, A. S., & Ablowitz, M. J. (1983). On the inverse scattering and direct linearizing transforms for the Kadomtsev-Petviashvili equation. Physics Letters A, 94(2), 67-70.
↑ Fokas, A. S., & Ablowitz, M. J. (1983). On the Inverse Scattering of the Time‐Dependent Schrödinger Equation and the Associated Kadomtsev‐Petviashvili (I) Equation. Studies in Applied Mathematics, 69(3), 211-228.
↑ ^15.0 ^15.1 Hirota, R., Ohta, Y., & Satsuma, J. (1988). Solutions of the Kadomtsev-Petviashvili equation and the two-dimensional Toda equations. Journal of the Physical Society of Japan, 57(6), 1901-1904.
↑ 松木平淳太, & 薩摩順吉. (1989). KP hierarchy の対称性と保存量 (ソリトン理論における広田の方法).
↑ Willox, R., Tokihiro, T., & Satsuma, J. (1997). Darboux and binary Darboux transformations for the nonautonomous discrete KP equation. Journal of Mathematical Physics, 38(12), 6455-6469.
↑ Isojima, S., Willox, R., & Satsuma, J. (2002). On various solutions of the coupled KP equation. Journal of Physics A: Mathematical and General, 35(32), 6893.
↑ ^19.0 ^19.1 Matsukidaira, J., Satsuma, J., & Strampp, W. (1990). Conserved quantities and symmetries of KP hierarchy. Journal of mathematical physics, 31(6), 1426-1434.
↑ Kajiwara, K., Matsukidaira, J., & Satsuma, J. (1990). Conserved quantities of two-component KP hierarchy. Physics Letters A, 146(3), 115-118.
↑ Date, E., Jimbo, M., Kashiwara, M., & Miwa, T. (1982). Transformation groups for soliton equations—Euclidean Lie algebras and reduction of the KP hierarchy—. Publications of the Research Institute for Mathematical Sciences, 18(3), 1077-1110.
↑ Date, E., Jimbo, M., Kashiwara, M., & Miwa, T. (1981). Operator Approach to the Kadomtsev-Petviashvili Equation–Transformation Groups for Soliton Equations III–. Journal of the Physical Society of Japan, 50(11), 3806-3812.
↑ Date, E., Jimbo, M., Kashiwara, M., & Miwa, T. (1982). Transformation groups for soliton equations: IV. A new hierarchy of soliton equations of KP-type. Physica D: Nonlinear Phenomena, 4(3), 343-365.
↑ Date, E., Jimbo, M., Kashiwara, M., & Miwa, T. (1982). Quasi-Periodic Solutions of the Orthogonal KP Equation—Transformation Groups for Soliton Equations V—. Publications of the Research Institute for Mathematical Sciences, 18(3), 1111-1119.
↑ Date, E., Jimbo, M., Kashiwara, M., & Miwa, T. (1981). KP hierarchies of orthogonal and symplectic type–Transformation groups for soliton equations VI–. Journal of the Physical Society of Japan, 50(11), 3813-3818.
↑ テンプレート:Cite report
↑ テンプレート:Cite journal

[1] Wazwaz, A. M. (2008). Solitons and singular solitons for the Gardner–KP equation. Applied Mathematics and Computation, 204(1), 162-169.

[2] Xu, B., & Liu, X. Q. (2009). Classification, reduction, group invariant solutions and conservation laws of the Gardner-KP equation. Applied mathematics and computation, 215(3), 1244-1250.

[3] Naz, R., Ali, Z., & Naeem, I. (2013). Reductions and new exact solutions of ZK, Gardner KP, and modified KP equations via generalized double reduction theorem. In Abstract and Applied Analysis (Vol. 2013). Hindawi.

[4] Jawad, A. J. A. M., Mirzazadeh, M., & Biswas, A. (2015). Dynamics of shallow water waves with Gardner–Kadomtsev–Petviashvili equation. Discrete and Continuous Dynamical Systems, Series S, 8(6), 1155-1164.

[5] Wazwaz, A. M., & El-Tantawy, S. A. (2017). Solving the $(3 + 1)$ -dimensional KP–Boussinesq and BKP–Boussinesq equations by the simplified Hirota’s method. Nonlinear Dynamics, 88(4), 3017-3021.

[6] Sun, B., & Wazwaz, A. M. (2018). General high–order breathers and rogue waves in the $(3 + 1)$ -dimensional KP–Boussinesq equation. Communications in Nonlinear Science and Numerical Simulation, 64, 1-13.

[7] Wazwaz, A. M. (2008). Multiple-soliton solutions for the Lax–Kadomtsev–Petviashvili (Lax–KP) equation. Applied Mathematics and computation, 201(1-2), 168-174.

[8] Tokihiro, T., Takahashi, D., & Matsukidaira, J. (2000). Box and ball system as a realization of ultradiscrete nonautonomous KP equation. Journal of Physics A: Mathematical and General, 33(3), 607.

[udkp-9] 9.0 ^9.1 Shinzawa, N., & Hirota, R. (2003). The Bäcklund transformation equations for the ultradiscrete KP equation. Journal of Physics A: Mathematical and General, 36(16), 4667.

[bkp-10] 10.0 ^10.1 新沢信彦, & 広田良吾. (2003). 超離散 KP 方程式, 超離散 BKP 方程式の Backlund 変換方程式 (可積分系研究の新展開: 連続・離散・超離散).

[11] Krichever, I. M., & Novikov, S. P. (1978). Holomorphic bundles over Riemann surfaces and the Kadomtsev—Petviashvili equation. I. Functional Analysis and Its Applications, 12(4), 276-286.

[12] Fokas, A. S., & Ablowitz, M. J. (1983). Method of solution for a class of multidimensional nonlinear evolution equations. Physical Review Letters, 51(1), 7.

[13] Fokas, A. S., & Ablowitz, M. J. (1983). On the inverse scattering and direct linearizing transforms for the Kadomtsev-Petviashvili equation. Physics Letters A, 94(2), 67-70.

[14] Fokas, A. S., & Ablowitz, M. J. (1983). On the Inverse Scattering of the Time‐Dependent Schrödinger Equation and the Associated Kadomtsev‐Petviashvili (I) Equation. Studies in Applied Mathematics, 69(3), 211-228.

[hos-15] 15.0 ^15.1 Hirota, R., Ohta, Y., & Satsuma, J. (1988). Solutions of the Kadomtsev-Petviashvili equation and the two-dimensional Toda equations. Journal of the Physical Society of Japan, 57(6), 1901-1904.

[16] 松木平淳太, & 薩摩順吉. (1989). KP hierarchy の対称性と保存量 (ソリトン理論における広田の方法).

[17] Willox, R., Tokihiro, T., & Satsuma, J. (1997). Darboux and binary Darboux transformations for the nonautonomous discrete KP equation. Journal of Mathematical Physics, 38(12), 6455-6469.

[18] Isojima, S., Willox, R., & Satsuma, J. (2002). On various solutions of the coupled KP equation. Journal of Physics A: Mathematical and General, 35(32), 6893.

[#1-19] 19.0 ^19.1 Matsukidaira, J., Satsuma, J., & Strampp, W. (1990). Conserved quantities and symmetries of KP hierarchy. Journal of mathematical physics, 31(6), 1426-1434.

[20] Kajiwara, K., Matsukidaira, J., & Satsuma, J. (1990). Conserved quantities of two-component KP hierarchy. Physics Letters A, 146(3), 115-118.

[21] Date, E., Jimbo, M., Kashiwara, M., & Miwa, T. (1982). Transformation groups for soliton equations—Euclidean Lie algebras and reduction of the KP hierarchy—. Publications of the Research Institute for Mathematical Sciences, 18(3), 1077-1110.

[22] Date, E., Jimbo, M., Kashiwara, M., & Miwa, T. (1981). Operator Approach to the Kadomtsev-Petviashvili Equation–Transformation Groups for Soliton Equations III–. Journal of the Physical Society of Japan, 50(11), 3806-3812.

[23] Date, E., Jimbo, M., Kashiwara, M., & Miwa, T. (1982). Transformation groups for soliton equations: IV. A new hierarchy of soliton equations of KP-type. Physica D: Nonlinear Phenomena, 4(3), 343-365.

[24] Date, E., Jimbo, M., Kashiwara, M., & Miwa, T. (1982). Quasi-Periodic Solutions of the Orthogonal KP Equation—Transformation Groups for Soliton Equations V—. Publications of the Research Institute for Mathematical Sciences, 18(3), 1111-1119.

[25] Date, E., Jimbo, M., Kashiwara, M., & Miwa, T. (1981). KP hierarchies of orthogonal and symplectic type–Transformation groups for soliton equations VI–. Journal of the Physical Society of Japan, 50(11), 3813-3818.

[26] テンプレート:Cite report

[27] テンプレート:Cite journal

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KP方程式

目次

変種

KP方程式に関連した業績のある研究者

海外

日本

関連項目

出典

参考文献

関連文献

和文

英文

外部リンク

ナビゲーションメニュー

KP方程式

変種

KP方程式に関連した業績のある研究者

海外

日本

関連項目

出典

参考文献

関連文献

和文

英文

外部リンク

ナビゲーション メニュー

検索

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