Corrigendum to “On quintic equations with a linear window” [Phys. Lett. A 380 (2016) 135–141]

Physics Letters A 380 (2016) 2122

Contents lists available at ScienceDirect

Physics Letters A www.elsevier.com/locate/pla

Corrigendum

Corrigendum to “On quintic equations with a linear window” [Phys. Lett. A 380 (2016) 135–141] Philip Rosenau School of Mathematics, Tel Aviv University, Tel Aviv, 69978, Israel

a r t i c l e

i n f o

a b s t r a c t

Article history: Received 31 January 2016 Accepted 1 February 2016 Available online 12 April 2016 Communicated by C.R. Doering

Corrigendum to “On quintic equations with a linear window” [Phys. Lett. A 380 (2016) 135–141]. © 2015 Elsevier B.V. All rights reserved.

The author regrets to inform that an erroneous merging of files deleted a multiplicative factor in a number of formulas. The corrected formulas are stated. Equations (13), (15) and the definition of V h , above Eq. (11), should be multiplied by A ω defined via

U = A ω (1 + V h ) where A ω =

1 + ω

(*)

2

In Equations (18), (19), (21), (24) and (27), A ω should replace λ. The respective equations thus read





. γ+

U = A ω 1 + u 1 cos( z) + u 2 cos(rz)



U (s) = A ω 1 −

U=

8 3

r2

cos( z)

r 2 − 1 cos(σ )

+

where z = γ− s and r = cos(r z) 

1

γ−

where z = γ− s and

r 2 − 1 cos(r σ )

(13)

. .

σ = γ− L ,

A ω cos4 ( z/2) for | z = sγ− | ≤ σ = π ,

(18)

U = 2 A ω [1 + 2 sin2 ( z/2)] cos4 ( z/2) for | z = sγ− | ≤ σ = π ,

A( z0 ) : U asymm = A ω



U = Aω 1 −

r2 r2



U = Aω 1 −

∗

3 cos( z0 )

cos( z)

+ 1 cos(σ ) r∗2

r2

8 cos( z/2 ± z0 )

−

cosh(r∗ z˜ )

+ 1 cosh(r∗ σ∗ )

+ 1 cosh(r σ )

−

1 r2 ∗

where δ∗ =

cos(˜z) 

+ 1 cos(σ∗ )

DOI of original article: http://dx.doi.org/10.1016/j.physleta.2015.09.045. E-mail address: [email protected]. http://dx.doi.org/10.1016/j.physleta.2016.02.004 0375-9601/© 2015 Elsevier B.V. All rights reserved.

(19)

cos3 ( z/2), z0 < π /2.

cosh(r z) 

1 r2

(15)

(21) 4r 2

(1 + r 2 )2

with δ∗ =

4r∗2

(24)

.

(1 + r∗2 )2

.

(27)