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Darboux transformations and exact solutions of nonlocal Kaup–Newell equations with variable coefficients 变系数非局部kap - newell方程的达布变换和精确解
IF 3.7 2区 数学
Applied Mathematics Letters Pub Date : 2025-01-09 DOI: 10.1016/j.aml.2025.109456
Chen Wang, Yue Shi, Weiao Yang, Xiangpeng Xin
{"title":"Darboux transformations and exact solutions of nonlocal Kaup–Newell equations with variable coefficients","authors":"Chen Wang, Yue Shi, Weiao Yang, Xiangpeng Xin","doi":"10.1016/j.aml.2025.109456","DOIUrl":"https://doi.org/10.1016/j.aml.2025.109456","url":null,"abstract":"This paper investigates an integrable nonlocal Kaup–Newell (NKN) equation with variable coefficients. Utilizing Lax pair theory, the construction of the variable coefficient NKN equation is presented for the first time, alongside a systematic analysis employing the Darboux transform technique. This approach explicitly derives the form of the nth-order Darboux transform, which is presented for the first time. The article offers a thorough explanation of the derivation process for the second-order Darboux transform using Cramer’s rule, further extending this to propose a general formula for the <mml:math altimg=\"si1.svg\" display=\"inline\"><mml:mi>n</mml:mi></mml:math>th Darboux transform applicable to multi-parameter scenarios. By applying a zero-seed solution, the exact solution of the variable coefficient NKN equation is obtained. To explore the influence of different coefficient functions on the solutions, specific coefficient functions are selected, and their corresponding graphical representations are analyzed, uncovering a range of solution types, including single soliton solutions, multi-solitons, rogue wave solutions, mixed twisted soliton solutions and breather wave solutions. Through the comprehensive analysis of these solutions, the study underscores the significant enhancement in modeling accuracy when time- and space-dependent coefficients are incorporated into the NKN equations, particularly in the context of simulating the dynamic behavior of nonlinear waves in real-world applications.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"18 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142990375","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Higher-order freak waves of the AB system revisited via a variable separation method 通过变量分离方法重新研究了AB系统的高阶异常波
IF 3.7 2区 数学
Applied Mathematics Letters Pub Date : 2025-01-07 DOI: 10.1016/j.aml.2025.109454
Minjie Dong, Xiubin Wang
{"title":"Higher-order freak waves of the AB system revisited via a variable separation method","authors":"Minjie Dong, Xiubin Wang","doi":"10.1016/j.aml.2025.109454","DOIUrl":"https://doi.org/10.1016/j.aml.2025.109454","url":null,"abstract":"In this work, we theoretically calculate higher-order freak wave solutions of the AB system through a Darboux transformation by a separation of variable method. Furthermore, the dynamics of first-order and second-order freak wave solutions are discussed with some illustrative graphics. In particular, we observe the emergence of a four peaky-shaped freak wave in the second component, which contrasts with the previously reported four eye-shaped waves.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"6 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142968144","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Elliptic Neumann problems with highly discontinuous nonlinearities 具有高度不连续非线性的椭圆Neumann问题
IF 3.7 2区 数学
Applied Mathematics Letters Pub Date : 2025-01-07 DOI: 10.1016/j.aml.2025.109455
Giuseppina D’Aguì, Valeria Morabito, Patrick Winkert
{"title":"Elliptic Neumann problems with highly discontinuous nonlinearities","authors":"Giuseppina D’Aguì, Valeria Morabito, Patrick Winkert","doi":"10.1016/j.aml.2025.109455","DOIUrl":"https://doi.org/10.1016/j.aml.2025.109455","url":null,"abstract":"This paper investigates nonlinear differential problems involving the <mml:math altimg=\"si1.svg\" display=\"inline\"><mml:mi>p</mml:mi></mml:math>-Laplace operator and subject to Neumann boundary value conditions whereby the right-hand side consists of a nonlinearity which is highly discontinuous. Using variational methods suitable for nonsmooth functionals, we prove the existence of at least two nontrivial weak solutions of such problems.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"21 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142968145","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Limit solutions of loop solitons for a compound WKI-SP equation 一类复合WKI-SP方程环孤子的极限解
IF 3.7 2区 数学
Applied Mathematics Letters Pub Date : 2025-01-06 DOI: 10.1016/j.aml.2024.109452
Gaizhu Qu, Junyang Zhang, Xiaorui Hu, Shoufeng Shen
{"title":"Limit solutions of loop solitons for a compound WKI-SP equation","authors":"Gaizhu Qu, Junyang Zhang, Xiaorui Hu, Shoufeng Shen","doi":"10.1016/j.aml.2024.109452","DOIUrl":"https://doi.org/10.1016/j.aml.2024.109452","url":null,"abstract":"We characterize the limit solutions of loop solitons for an integrable compound equation which is a mix of the Wadati-Konno-Ichikawa (WKI) equation and the short-pulse (SP) equation. We do so by taking an ingenious limit on the <mml:math altimg=\"si1.svg\" display=\"inline\"><mml:mi>τ</mml:mi></mml:math>-function derived from Hirota’s bilinear equations of the mKdV-SG (modified Korteweg–de Vries and sine-Gordon) equation. By virtue of a hodograph transformation, we compute the limit solution of 2-loop (noted as <mml:math altimg=\"si45.svg\" display=\"inline\"><mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mo>−</mml:mo><mml:mi>l</mml:mi><mml:mi>o</mml:mi><mml:mi>o</mml:mi><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:math>) soliton and discuss the interactions between two <mml:math altimg=\"si45.svg\" display=\"inline\"><mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mo>−</mml:mo><mml:mi>l</mml:mi><mml:mi>o</mml:mi><mml:mi>o</mml:mi><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:math> solitons in detail. One singlevalued and two nonsinglevalued limit solutions of 2-breather solution are presented at last.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"77 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142968148","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Energy of steady periodic equatorial water waves in two-layer flows 两层流中稳定周期赤道水波的能量
IF 3.7 2区 数学
Applied Mathematics Letters Pub Date : 2025-01-04 DOI: 10.1016/j.aml.2024.109450
Xun Wang, Sanling Yuan, Jin Zhao
{"title":"Energy of steady periodic equatorial water waves in two-layer flows","authors":"Xun Wang, Sanling Yuan, Jin Zhao","doi":"10.1016/j.aml.2024.109450","DOIUrl":"https://doi.org/10.1016/j.aml.2024.109450","url":null,"abstract":"In this paper, we present the Euler equation of steady periodic equatorial water waves in two-layer flows with different densities and generalise the two Stokes’ definitions for the velocity of the wave propagation. We further demonstrate that the excess potential energy density of nonlinear equatorial two-layer waves is always positive, while the excess kinetic energy density is negative.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"22 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2025-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142968149","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On a Camassa–Holm type equation describing the dynamics of viscous fluid conduits 描述粘性流体管道动力学的Camassa-Holm型方程
IF 3.7 2区 数学
Applied Mathematics Letters Pub Date : 2025-01-04 DOI: 10.1016/j.aml.2024.109443
Rafael Granero-Belinchón
{"title":"On a Camassa–Holm type equation describing the dynamics of viscous fluid conduits","authors":"Rafael Granero-Belinchón","doi":"10.1016/j.aml.2024.109443","DOIUrl":"https://doi.org/10.1016/j.aml.2024.109443","url":null,"abstract":"In this note we derive a new nonlocal and nonlinear dispersive equations capturing the main dynamics of a circular interface separating a light, viscous fluid rising buoyantly through a heavy, more viscous, miscible fluid at small Reynolds numbers. This equation that we termed the <mml:math altimg=\"si1.svg\" display=\"inline\"><mml:mrow><mml:mi>g</mml:mi><mml:mo>−</mml:mo></mml:mrow></mml:math>model shares some common structure with the Camassa–Holm equation but has additional nonlocal effects. For this new PDE we study the well-posedness together with the existence of periodic traveling waves. Furthermore, we also show some numerical simulations suggesting the finite time singularity formation.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"50 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2025-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142968150","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A strong mass conservative finite element method for the Navier–Stokes/Darcy coupled system Navier-Stokes /Darcy耦合系统的强质量保守有限元方法
IF 3.7 2区 数学
Applied Mathematics Letters Pub Date : 2025-01-03 DOI: 10.1016/j.aml.2024.109447
Jessika Camaño, Ricardo Oyarzúa, Miguel Serón, Manuel Solano
{"title":"A strong mass conservative finite element method for the Navier–Stokes/Darcy coupled system","authors":"Jessika Camaño, Ricardo Oyarzúa, Miguel Serón, Manuel Solano","doi":"10.1016/j.aml.2024.109447","DOIUrl":"https://doi.org/10.1016/j.aml.2024.109447","url":null,"abstract":"We revisit the continuous formulation introduced in Discacciati and Oyarzúa (2017) for the stationary Navier–Stokes/Darcy (NSD) coupled system and propose an equivalent scheme that does not require a Lagrange multiplier to enforce the continuity of normal velocities at the interface. Building on this formulation and following a similar approach to Kanschat and Rivière (2010), we derive a mass-conservative, <mml:math altimg=\"si1.svg\" display=\"inline\"><mml:mrow><mml:mi mathvariant=\"bold\">H</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant=\"normal\">div</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>–conforming finite element method for the NSD system.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"21 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142968153","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Uniqueness of solution for incompressible inhomogeneous Navier–Stokes equations in dimension two 二维不可压缩非齐次Navier-Stokes方程解的唯一性
IF 3.7 2区 数学
Applied Mathematics Letters Pub Date : 2025-01-03 DOI: 10.1016/j.aml.2024.109449
Yelei Guo, Chinyin Qian
{"title":"Uniqueness of solution for incompressible inhomogeneous Navier–Stokes equations in dimension two","authors":"Yelei Guo, Chinyin Qian","doi":"10.1016/j.aml.2024.109449","DOIUrl":"https://doi.org/10.1016/j.aml.2024.109449","url":null,"abstract":"The global existence of solution for 2D inhomogeneous incompressible Navier–Stokes equations is established by Abidi et al. (2024), and the uniqueness of solution is also investigated under some additional conditions on initial density. The purpose of this paper is to obtain the uniqueness of the solution without any additional assumptions on the initial density in case of <mml:math altimg=\"si1.svg\" display=\"inline\"><mml:mrow><mml:mn>2</mml:mn><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">≤</mml:mo><mml:mi>p</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">&lt;</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math>. The key strategy is to establish a new estimate of solution in Lagrangian coordinates.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"29 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142968151","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A free-parameter alternating triangular splitting iteration method for time-harmonic parabolic problems 时谐抛物问题的自由参数交替三角分裂迭代法
IF 3.7 2区 数学
Applied Mathematics Letters Pub Date : 2025-01-01 DOI: 10.1016/j.aml.2024.109429
Chengliang Li, Jiashang Zhu, Changfeng Ma
{"title":"A free-parameter alternating triangular splitting iteration method for time-harmonic parabolic problems","authors":"Chengliang Li, Jiashang Zhu, Changfeng Ma","doi":"10.1016/j.aml.2024.109429","DOIUrl":"https://doi.org/10.1016/j.aml.2024.109429","url":null,"abstract":"Based on the triangular splitting technique, we introduce a free-parameter alternating triangular splitting (FPATS) method for solving block two-by-two linear systems with applications to time-harmonic parabolic models. In addition, we demonstrate that the FPATS method is unconditionally convergent and outperforms other methods. Numerical results are provided to show the practicality and efficiency of our method.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"25 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142929259","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Time periodic solution for a system of spatially inhomogeneous wave equations with nonlinear couplings 具有非线性耦合的空间非齐次波动方程系统的时间周期解
IF 3.7 2区 数学
Applied Mathematics Letters Pub Date : 2024-12-30 DOI: 10.1016/j.aml.2024.109448
Jiayu Deng, Jianhua Liu, Shuguan Ji
{"title":"Time periodic solution for a system of spatially inhomogeneous wave equations with nonlinear couplings","authors":"Jiayu Deng, Jianhua Liu, Shuguan Ji","doi":"10.1016/j.aml.2024.109448","DOIUrl":"https://doi.org/10.1016/j.aml.2024.109448","url":null,"abstract":"This paper is concerned with the existence of periodic solution for a system of spatially inhomogeneous wave equations with nonlinear couplings. The main contribution of this research lies in the fact that the coupled terms are nonlinear. For the periods having the form <mml:math altimg=\"si1.svg\" display=\"inline\"><mml:mrow><mml:mi>T</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">=</mml:mo><mml:mn>2</mml:mn><mml:mi>π</mml:mi><mml:mfrac><mml:mrow><mml:mn>2</mml:mn><mml:mi>a</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:mfrac></mml:mrow></mml:math> (<mml:math altimg=\"si2.svg\" display=\"inline\"><mml:mrow><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mi>b</mml:mi></mml:mrow></mml:math> are positive integers), by applying the dual variational method, we establish the existence of the time periodic solution under some Sturm–Liouville boundary conditions. To our knowledge, there is rarely papers focus on the existence of periodic solution for a system of spatially inhomogeneous wave equations with nonlinear couplings.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"3 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142929216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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