{"title":"新[式略]维广义卡多姆采夫-彼得维亚什维利方程的 Dbar-dressing 方法","authors":"Zhenjie Niu, Biao Li","doi":"10.1016/j.aml.2024.109411","DOIUrl":null,"url":null,"abstract":"The primary purpose of this work is to consider a <mml:math altimg=\"si6.svg\" display=\"inline\"><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>-dimensional generalized KP equation via <mml:math altimg=\"si2.svg\" display=\"inline\"><mml:mover accent=\"true\"><mml:mrow><mml:mi>∂</mml:mi></mml:mrow><mml:mrow><mml:mo>̄</mml:mo></mml:mrow></mml:mover></mml:math>-dressing method. Using the Fourier transform and Fourier inverse transform, we give the expression of the Green function for spatial spectral problem. Then, we choose two linear independent eigenfunctions and calculate the <mml:math altimg=\"si2.svg\" display=\"inline\"><mml:mover accent=\"true\"><mml:mrow><mml:mi>∂</mml:mi></mml:mrow><mml:mrow><mml:mo>̄</mml:mo></mml:mrow></mml:mover></mml:math> derivative, a <mml:math altimg=\"si2.svg\" display=\"inline\"><mml:mover accent=\"true\"><mml:mrow><mml:mi>∂</mml:mi></mml:mrow><mml:mrow><mml:mo>̄</mml:mo></mml:mrow></mml:mover></mml:math> problem arises naturally. Based on the symmetry of the Green function, we give a standard <mml:math altimg=\"si2.svg\" display=\"inline\"><mml:mover accent=\"true\"><mml:mrow><mml:mi>∂</mml:mi></mml:mrow><mml:mrow><mml:mo>̄</mml:mo></mml:mrow></mml:mover></mml:math> equation, and its solution is expressed by the Cauchy formula.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"47 1","pages":""},"PeriodicalIF":2.9000,"publicationDate":"2024-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Dbar-dressing method for a new [formula omitted]-dimensional generalized Kadomtsev–Petviashvili equation\",\"authors\":\"Zhenjie Niu, Biao Li\",\"doi\":\"10.1016/j.aml.2024.109411\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The primary purpose of this work is to consider a <mml:math altimg=\\\"si6.svg\\\" display=\\\"inline\\\"><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo linebreak=\\\"goodbreak\\\" linebreakstyle=\\\"after\\\">+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>-dimensional generalized KP equation via <mml:math altimg=\\\"si2.svg\\\" display=\\\"inline\\\"><mml:mover accent=\\\"true\\\"><mml:mrow><mml:mi>∂</mml:mi></mml:mrow><mml:mrow><mml:mo>̄</mml:mo></mml:mrow></mml:mover></mml:math>-dressing method. Using the Fourier transform and Fourier inverse transform, we give the expression of the Green function for spatial spectral problem. Then, we choose two linear independent eigenfunctions and calculate the <mml:math altimg=\\\"si2.svg\\\" display=\\\"inline\\\"><mml:mover accent=\\\"true\\\"><mml:mrow><mml:mi>∂</mml:mi></mml:mrow><mml:mrow><mml:mo>̄</mml:mo></mml:mrow></mml:mover></mml:math> derivative, a <mml:math altimg=\\\"si2.svg\\\" display=\\\"inline\\\"><mml:mover accent=\\\"true\\\"><mml:mrow><mml:mi>∂</mml:mi></mml:mrow><mml:mrow><mml:mo>̄</mml:mo></mml:mrow></mml:mover></mml:math> problem arises naturally. Based on the symmetry of the Green function, we give a standard <mml:math altimg=\\\"si2.svg\\\" display=\\\"inline\\\"><mml:mover accent=\\\"true\\\"><mml:mrow><mml:mi>∂</mml:mi></mml:mrow><mml:mrow><mml:mo>̄</mml:mo></mml:mrow></mml:mover></mml:math> equation, and its solution is expressed by the Cauchy formula.\",\"PeriodicalId\":55497,\"journal\":{\"name\":\"Applied Mathematics Letters\",\"volume\":\"47 1\",\"pages\":\"\"},\"PeriodicalIF\":2.9000,\"publicationDate\":\"2024-12-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Mathematics Letters\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1016/j.aml.2024.109411\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1016/j.aml.2024.109411","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Dbar-dressing method for a new [formula omitted]-dimensional generalized Kadomtsev–Petviashvili equation
The primary purpose of this work is to consider a (2+1)-dimensional generalized KP equation via ∂̄-dressing method. Using the Fourier transform and Fourier inverse transform, we give the expression of the Green function for spatial spectral problem. Then, we choose two linear independent eigenfunctions and calculate the ∂̄ derivative, a ∂̄ problem arises naturally. Based on the symmetry of the Green function, we give a standard ∂̄ equation, and its solution is expressed by the Cauchy formula.
期刊介绍：
The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.
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