The Proteas left Johannesburg on Saturday for two Tests and three one-day internationals against India, the world's number one ranked Test nation, after Arthur quit on Wednesday due to differences with the South African board.
“It's been an emotional week and not many teams go to India and win,” Smith told a news conference on Saturday.
“But our record in the sub-continent is solid and the players who have been part of the set-up for a while have dealt with a few difficult things in recent years and handled them very well.
“I expect them to be as professional as normal, and I'm looking to them for responsibility and guidance for the youth,” Smith said. Former fast bowler Corrie van Zyl, an assistant coach for the national team between 1998 and 2003, has replaced Arthur on an interim basis.
“My experience of things like the last week is that it builds a team rather than tears it apart,” Van Zyl said. “I was part of the management team when the Hansie Cronje issue came about and sometimes those things just pull a team together.”
Former South African captain Cronje admitted in 2000 to receiving about $130,000 from bookmakers to influence the course of matches. He was banned for life.
“Obviously the players have to deal with their emotions, but it's a very important series and we need to focus on our preparations,” Van Zyl said.
South Africa will play a two-day warm-up match against an Indian Board President's XI in Nagpur starting on Tuesday before the first Test in the same city, which begins on Feb 6.
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