On connection between the order of a stationary one-dimensional dispersive equation and the growth of its convective term

Larkin, Nikolai A.; Luchesi, Jackson

doi:10.5269/bspm.41478

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Cited by 2 publications

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“…. , l − 1 for (1.1) were imposed, see [20,22]. Different kind of boundary conditions for KdV and Kawahara equations was considered in [8,17,21,23].…”

Section: Introductionmentioning

confidence: 99%

Formulation of Problems for Stationary Dispersive Equations of Higher Orders on Bounded Intervals with General Boundary Conditions

Larkin

Luchesi

2020

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“…. , l − 1 for (1.1) were imposed, see [20,22]. Different kind of boundary conditions for KdV and Kawahara equations was considered in [8,17,21,23].…”

Section: Introductionmentioning

confidence: 99%

Formulation of Problems for Stationary Dispersive Equations of Higher Orders on Bounded Intervals with General Boundary Conditions

Larkin

Luchesi

2020

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Initial-Boundary Value Problems for Generalized Dispersive Equations of Higher Orders Posed on Bounded Intervals

Larkin

Luchesi

2019

Appl Math Optim

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Initial-boundary value problems for nonlinear dispersive equations of evolution of order 2l + 1, l ∈ N with a convective term of the form u k u x , k ∈ N have been considered on intervals (0, L), L ∈ (0, +∞). The existence and uniqueness of local regular solutions have been established.where x ∈ (0, L), Q T = (0, T ) × (0, L); l, k ∈ N; T, L are real positive numbers. This equation includes as special cases classical dispersive equations: when l = k = 1, we have the well-known Kortewegde Vries (KdV) equation, see [15,20,31], and when k = 1, l = 2, we have the Kawahara equation [5,16,23]. For k = 1, the Cauchy problem for dispersive equations of higher orders has been studied in [3,6,11,12,17,28,32] and initial boundary value problems have been studied in [4,5,7,23,30]. Although dispersive equations were deduced for the whole real line, necessity to calculate numerically the Cauchy problem, approximating the real line by finite intervals [4], implies to study initial-boundary value problems posed on bounded and unbounded intervals, [5,7,19,21,23]. What concerns (1.1) with k > 1, l = 1, called generalized Korteweg-de Vries equations, the Cauchy problem for (1.1) has been studied in [8,9,10,18,25,26], where was proved that for k = 4, called the critical case, the initial

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On connection between the order of a stationary one-dimensional dispersive equation and the growth of its convective term

Cited by 2 publications

References 29 publications

Formulation of Problems for Stationary Dispersive Equations of Higher Orders on Bounded Intervals with General Boundary Conditions

Formulation of Problems for Stationary Dispersive Equations of Higher Orders on Bounded Intervals with General Boundary Conditions

Initial-Boundary Value Problems for Generalized Dispersive Equations of Higher Orders Posed on Bounded Intervals

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